Sum this series...its fairly fun

$\displaystyle \sum_{n=1}^{\infty}\frac{(-1)^{n+1}n^2}{n^3+1}$

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- Nov 5th 2008, 02:50 PMMathstud28Series
Sum this series...its fairly fun

$\displaystyle \sum_{n=1}^{\infty}\frac{(-1)^{n+1}n^2}{n^3+1}$ - Nov 7th 2008, 12:23 PMMathstud28
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.