Power Series (Complex Analysis)

Find the radius of convergence of the given power series.

(1) $\displaystyle {\sum_{k=0}}^{\infty}$ $\displaystyle \frac{(k!)^2}{(2k)!}(z-2)^k$

(2) $\displaystyle {\sum_{j=0}}^{\infty}$ $\displaystyle \frac{z^{3j}}{2^j}$

I'm not sure how to use the theorems given in my book to solve these.

Theorem: Suppose that $\displaystyle {\sum_0}^{\infty}$$\displaystyle a_n(z-z_0)^n$ is a power series with a positive or infinite radius of convergence R.

(a) If $\displaystyle lim_{n \to\infty} |a_{n+1}/a_n|$ exists, then $\displaystyle \frac{1}{R} = lim_{n \to\infty}|\frac{a_{n+1}}{a_n}|$

(b) If $\displaystyle lim_{n\to\infty}\sqrt[n]{|a_n|}$ exists, then $\displaystyle \frac{1}{R} =lim_{n\to\infty}\sqrt[n]{|a_n|}$

Any help would be appreciated, thanks!