So I have a question about the convergence of a series here:
It says:
Find the radius and interval of convergence, then identify the values of $x$ for which the series converges absolutely and conditionally
$\displaystyle \sum_{n=1}^{\infty} (\text{csch}(n))x^n$
I already found the radius of convergence. It's $e$. The interval of convergence is $(-e,e)$. I checked the endpoints and they both diverge.
So I know for all values of $x$ on the interval $(-e,e)$, the series converges absolutely. What about the conditional convergence though? How do I show that part? I'm a little confused on that. I don't even think that would ever happen.