Index
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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 values
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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