Question

What is the radius of convergence of the power series (((2n)!x^(n))/((2n-1)!)), and what is its interval of convergence?

I used the ratio test and found that the radius of convergence is 0, as it is impossible for the absolute value of infinity to be less than 1. I am not sure I found the radius correctly though, as I am asked what the interval of convergence is. This confuses me because it doesn't seem that the power series converges at all.

Thanks!