# Find the radius of convergence

1. Dec 14, 2008

### JulioMarcos

The problem statement, all variables and given/known data
Find the radius of convergence of the Series:
$$\sum_{i=1}^{\infty}\frac{(2n)!x^n}{(n!)^2}$$

The attempt at a solution
I used the Ratio Test but I always get L = $$|\frac{2x}{n+1}|$$

The answer is 1/4. I think im mistaking with factorial.

2. Dec 14, 2008

### JulioMarcos

Solved. The problem was tha
(2(n+1))! = (2n + 2)(2n + 1)(2n)!
and I was doing (2(n+1))! = (2n + 2)(2n)!
because i thought you should distribute the 2

3. Dec 14, 2008

### Mthees08

Ah it is always good to find your own mistake. Off the bat that was my guess... Sadly I got in the thread too late.