Limsupremum calculation horrible difficulty

1. Oct 23, 2010

betty2301

1. The problem statement, all variables and given/known data
Calculate the radius of convergence of $\sum_{n=0}^\infty a_{n}z^{2n}$
let $\sum_{n=0}^\infty a_{n}z^{n}$with radius R

2. Relevant equations
$\limsup|a_n|^{\frac{1}{n}}=\limsup |\frac{a_{n+1}}{a_n}|$

3. The attempt at a solution
$$\limsup|a_n|^{\frac{1}{n}}=\lim_{k\to\infty}|a_{2k}|^{\frac{1}{2k}}$$
then how to write the "ratio".............