I have encountered this alternating series and I want to know how we can prove that
$$\sum_{n=0}^\infty\frac{(-1)^{n+1}n^2}{n^{3}+1}=\frac{1}{3}-\frac{1}{3}\ln(2)+\frac{\pi}{3}\sinh\left(\pi\frac{\sqrt{3}}{2}\right)$$
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Can you prove the converse using Taylor Expansion? – Saketh Malyala Aug 08 '18 at 04:11
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3Even better, can you give us some context, or some of your own thoughts about the problem? See here: https://math.stackexchange.com/help/how-to-ask – Robert Howard Aug 08 '18 at 04:14