How do i show the following series from n=1 to infinity converges?(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\sum\frac{(n!)^2}{(2n)!}[/tex]

what i did was apply the ratio test so i ended up with

the limit as n--> infinity of

[tex]\frac{((n+1)^2)(n!)^2}{(2(n+1))!(2n)!}(\frac{((2n)!}{(n!)^2})[/tex]

then after the cancelation of the factorial terms, this limit goes to infinity...

however this series converges by the answer i have for this problem. where did i go wrong?

thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Convergence of series

**Physics Forums | Science Articles, Homework Help, Discussion**