Determine the radius of convergence

(a) $\displaystyle{\sum_{n=1}^\infty \frac{z^n}{2^n n^2}}$

(b) $\displaystyle{\sum_{n=1}^\infty \frac{z^{3n} (3n)!}{20^n (2n)! }}$

If the radius of convergence is $R$, $0<R< \infty$, determine for each $z\colon |z|=R$ if this series converges.