I have to evaluate pointwise/uniform/total convergence of this series and I didn't quite understand how to do it. $$\sum_{k=2}^{+\infty}{\ln k \over 2+\sin k}x^k$$ For pointwise convergence: it clearly diverges if $|x|\gt 1$ and converges if $x=0$.
EDIT: I managed to do everything else but still don't understand what happens in $x=-1$. Help?