(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex]\frac{1^2*3^2*5^2...(2n-1)^2}{2^2*4^2*6^2...(2n)^2}<\frac{1}{2n+1}[/itex]

Edit:Must be proven without using induction.

2. Relevant equations

3. The attempt at a solution

I understand the LHS is the same thing as

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

And (2n)!! = [itex]k!2^k[/itex] & (2n-1)!! = [itex]\frac{(2k)!}{k!2^k}[/itex]

I've tried substituting and it doesn't seem to help. Any ideas? Thanks.

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# Homework Help: Inequality with factorial

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