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

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# Homework Help: Convergence of series

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