Determine if the series is convergent $$\sum_{n=0}^\infty \frac {\ln n} { \sinh (in)}$$
I am stuck here guys, any hint? :/ I have tried abel test, but it didn't help. Edit: Jose reminded me to check the main part's limit, which isn't zero.
2026-03-30 01:33:14.1774834394
determine convergence of complex set ∑ ln(n) / sinh(in)
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It diverges, since you don't have $\displaystyle\lim_{n\to\infty}\frac{\ln n}{\sinh(in)}=0$. In fact$$\left|\frac{\ln n}{\sinh(in)}\right|=\left|\frac{\ln n}{i\sin n}\right|=\left|\frac{\ln n}{\sin n}\right|\geqslant\ln n.$$