Index
stringlengths 1
5
| Challenge
stringlengths 41
1.55k
| Answer in Latex
stringclasses 122
values | Answer in Sympy
stringlengths 1
774
| Variation
stringclasses 31
values | Source
stringclasses 61
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301 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
302 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
303 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
304 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
305 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
306 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
307 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
308 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
309 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
310 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
311 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
312 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
313 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
314 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
315 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
316 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
317 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
318 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
319 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
320 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
321 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
322 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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323 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
324 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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325 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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326 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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327 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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328 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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329 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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330 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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331 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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332 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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333 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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334 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-All-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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335 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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336 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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337 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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338 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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339 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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340 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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341 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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342 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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343 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i A x} - e^{- i A x}\right)}{2 \sin{\left(A x \right)}}\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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344 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i A x} + 1\right) \tan{\left(A x \right)}}{\left(1 - e^{4 i A x}\right) \left(1 - \tan^{2}{\left(A x \right)}\right)}\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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345 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(3\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*3/6 | Numeric-One-1 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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346 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(35\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*35/6 | Numeric-One-2 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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347 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(789\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*789/6 | Numeric-One-3 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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348 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(5806\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*5806/6 | Numeric-One-4 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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349 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(12902\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*12902/6 | Numeric-One-5 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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350 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(668529\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*668529/6 | Numeric-One-6 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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351 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(5503043\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*5503043/6 | Numeric-One-7 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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352 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(37840584\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*37840584/6 | Numeric-One-8 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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353 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(426865087\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*426865087/6 | Numeric-One-9 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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354 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(7755469684\right) n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*7755469684/6 | Numeric-One-10 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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355 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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356 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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357 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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358 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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359 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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360 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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361 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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362 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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363 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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364 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
365 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(9\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*9/6 | Numeric-One-1 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
366 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(79\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*79/6 | Numeric-One-2 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
367 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(222\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*222/6 | Numeric-One-3 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
368 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(6013\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*6013/6 | Numeric-One-4 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
369 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(99455\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*99455/6 | Numeric-One-5 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
370 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(370566\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*370566/6 | Numeric-One-6 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
371 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(6925325\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*6925325/6 | Numeric-One-7 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
372 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(69770590\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*69770590/6 | Numeric-One-8 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
373 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(622741480\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*622741480/6 | Numeric-One-9 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
374 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(5729172119\right) n \cdot ( x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))*5729172119/6 | Numeric-One-10 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
375 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
376 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
377 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
378 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
379 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
380 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
381 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
382 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
383 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Easy | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
384 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6 | Equivalence-One-Hard | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
385 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(2\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(2\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*2**n, (n, 2, oo))/6 | Numeric-One-1 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
386 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(54\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(54\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*54**n, (n, 2, oo))/6 | Numeric-One-2 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
387 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(867\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(867\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*867**n, (n, 2, oo))/6 | Numeric-One-3 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
388 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(3801\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(3801\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*3801**n, (n, 2, oo))/6 | Numeric-One-4 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
389 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(57767\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(57767\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*57767**n, (n, 2, oo))/6 | Numeric-One-5 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
390 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(571517\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(571517\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*571517**n, (n, 2, oo))/6 | Numeric-One-6 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
391 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(5409610\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(5409610\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*5409610**n, (n, 2, oo))/6 | Numeric-One-7 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
392 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(56761193\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(56761193\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*56761193**n, (n, 2, oo))/6 | Numeric-One-8 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
393 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(786200900\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(786200900\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*786200900**n, (n, 2, oo))/6 | Numeric-One-9 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
394 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(8382186640\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( \left(8382186640\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*8382186640**n, (n, 2, oo))/6 | Numeric-One-10 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
395 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(5\right) n \cdot ( \left(8\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(7\right) n \cdot ( \left(8\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*8**n, (n, 2, oo))*7*5/6 | Numeric-All-1 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
396 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(76\right) n \cdot ( \left(59\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(43\right) n \cdot ( \left(59\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*59**n, (n, 2, oo))*43*76/6 | Numeric-All-2 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
397 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(769\right) n \cdot ( \left(763\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(297\right) n \cdot ( \left(763\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*763**n, (n, 2, oo))*297*769/6 | Numeric-All-3 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
398 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(8937\right) n \cdot ( \left(5433\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(7365\right) n \cdot ( \left(5433\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*5433**n, (n, 2, oo))*7365*8937/6 | Numeric-All-4 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
399 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(39530\right) n \cdot ( \left(68250\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(80927\right) n \cdot ( \left(68250\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*68250**n, (n, 2, oo))*80927*39530/6 | Numeric-All-5 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
|
400 | Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(329249\right) n \cdot ( \left(524768\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(314629\right) n \cdot ( \left(524768\right) x)^n\right$ | Sum(n*x**n*(n**2 - 1)*524768**n, (n, 2, oo))*314629*329249/6 | Numeric-All-6 | U-Math
sequences_series
fb6418ae-3440-4258-9388-89d799fd859a |
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