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## Homework Statement:

- using ratio test verify if converges

## Relevant Equations:

- convergence tests

## \sum_{n=0}^\infty \frac {(2n)!}{(n!)^2} ##

##\lim_{n \rightarrow +\infty} {\frac {a_{n+1}} {a_n}}##

that becomes

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

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

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

then i don't know what else i can do

##\lim_{n \rightarrow +\infty} {\frac {a_{n+1}} {a_n}}##

that becomes

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

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

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

then i don't know what else i can do

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