Originally Posted by

**Shananay** This problem is tripping me up:

$\displaystyle

\sum_{n=1}^{\infty} \frac {(n!)^2}{(2n)!}

$

I'm trying to use the ratio test to see if it converges/diverges and am getting:

$\displaystyle

\lim_{n \rightarrow\ \infty} \frac{((n+1)!)^2}{(2(n+1))!}\times\frac{(2n)!}{(n! )^2}

$

I'm assuming the work is correct so far, and that the ratio test is the right test to use, but I really have no idea where to go from here. I'd like to be able to cancel some stuff but I think I'm lacking a good understanding of how these factorials relate to each other and how to work with them squared. Any help appreciated.