How to prove that $4\sum_{n=1}^{\infty}\frac{1-\cos(n\pi)}{n\sinh(n\pi)}=\ln2$?

Asked Aug 14 '19 at 07:59

Active Aug 14 '19 at 08:48

Viewed 143 times

This problem is equal to prove that $$8\sum_{n=1}^{\infty}\frac{1}{(2n-1)\sinh((2n-1)\pi)}=\ln2$$ I try to use Fourier transform but failed,how to deal with it?

edited Aug 14 '19 at 08:48

Zacky

27,674

asked Aug 14 '19 at 07:59

du gu qq bl

Thanks in advance! – du gu qq bl Aug 14 '19 at 08:30
1

You can find it here: https://math.stackexchange.com/q/304390/515527 (I missclicked when I tried to mark it as a duplicate and now it shows this: https://math.stackexchange.com/q/304681/515527). – Zacky Aug 14 '19 at 08:45

How to prove that $4\sum_{n=1}^{\infty}\frac{1-\cos(n\pi)}{n\sinh(n\pi)}=\ln2$?

0 Answers0