how to find its radius of convergence, it tried the ratio test
but it doesnt work
I think you'll find that $\displaystyle \lim_{n \rightarrow \infty} \frac{(n+1)^{\sqrt{n+1}}}{n^{\sqrt{n}}} = 1$.
So the ratio test forces the requirement |z| < 1. Then you must test the cases z = 1 and z = -1 for convergence, which should be very simple to do .....
So the ratio test forces the requirement |z| < 1. Then you must test the cases z = 1 and z = -1 for convergence, which should be very simple to do .....
No. $\displaystyle z$ is complex so $\displaystyle |z|=1\implies z = e^{i\theta}$. There are infinitely many points to check.