Find the radius of convergence

[JulioMarcos]

Homework Statement
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 I am mistaking with factorial.

 

[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

 

[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.