Sum this series...its fairly fun $\displaystyle \sum_{n=1}^{\infty}\frac{(-1)^{n+1}n^2}{n^3+1}$
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Hint: The answer is $\displaystyle \frac{1}{3}\left(1-\ln(2)+\frac{\pi}{\cosh\left(\frac{\sqrt{3}\pi}{2} \right)}\right)$. Now prove it.
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