Complex Radius of Convergence

[monomocoso]

Someone please check my work:

Find the radius of convergence for:

a) \(\displaystyle \sum_{n=0}^{\infty}a_n z^{2n}\)

b) \(\displaystyle \sum_{n=0}^{\infty}a^2_n z^{2n}\)

c) \(\displaystyle \sum_{n=0}^{\infty}a_n z^{n}
\)

d) \(\displaystyle \sum_{n=0}^{\infty}\frac {a_n z^n}{n!}
\)
I have found \(\displaystyle \sqrt{R}\) for a and \(\displaystyle R^2\) for b. For c I have \(\displaystyle R}\) and for d I have \(\displaystyle \infty\)