check an answer FOR RADIUS OF CONV

Hello, I need to check my answer:

The problem asks me to find the radius of convergence for:

inf

Sum

n=1

(-1)^n * x^(2n+1)

_________________

(2n+1)!

I preform the ratio test, use bn+1/bn...replace alln with n+1...times by reciprocal, etc...the typical method and get:

1/2|x^2/(n+1)(2n+3)|

Taking the limit, the answer = 0....thus the radius is then INFINTE.

So the radius is Infinity. If we were asked, then the int of convergence is (-inf, inf).

Is my answer right?