Answer
$\frac{1}{4n^2+2n}$
Work Step by Step
$\frac{(2n-1)!}{(2n+1)!}=\frac{(2n-1)!}{(2n+1)(2n)(2n-1)!}=\frac{1}{(2n+1)(2n)}=\frac{1}{4n^2+2n}$
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