The problem:Find the radius and interval of convergence.

$\displaystyle \[\sum_{1}^{\infty}\frac{2^n(x-2^n)}{(n+2)!}\]$

The attempt:

I basically did the ratio test and it equaled 0. So does R = $\displaystyle \infty$ and I = $\displaystyle (-\infty,\infty)$?