I was trying to figure out $\sum^\infty_{n=0}\frac{1}{n^4-1}$ and I got $$\sum^\infty_{n=0} \frac{1}{n^2+1}$$
As a part of it, I've tied to solve it using partial fractions with complex numbers with no success.
Do any of you know how to derive the solution?(I got $\frac{1}{2}(1+\pi\coth(\pi))$ from wolfram alpha)
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razivo
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1http://dlmf.nist.gov/4.36.E3 – Gary Dec 09 '20 at 11:52
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1Does this answer your question? Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$ Found using Approach0. – Toby Mak Dec 09 '20 at 11:54
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Yes, I've tried searching, I'm unsure why I didn't find it. – razivo Dec 09 '20 at 13:32