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Show by induction that (2n1)!!/(2n)!! <= 1/(3n+1) for all n
Show by induction that [itex](\frac{1\cdot3\cdot5\cdot\cdot\cdot(2n1)}{2\cdot4\cdot6\cdot\cdot\cdot2n})^2[/itex] [itex]\leq[/itex][itex]\frac{1}{3n+1}[/itex] for n=1,2,3, ...
It might not really be relevant, but I've attached my work. I tried to subprove something by induction to help my principal induction, but I got something that was harder than the original.
P.S. I tried using the Physics forums android app, but I couldn't figure out how to post.
Homework Statement
Show by induction that [itex](\frac{1\cdot3\cdot5\cdot\cdot\cdot(2n1)}{2\cdot4\cdot6\cdot\cdot\cdot2n})^2[/itex] [itex]\leq[/itex][itex]\frac{1}{3n+1}[/itex] for n=1,2,3, ...
The Attempt at a Solution
It might not really be relevant, but I've attached my work. I tried to subprove something by induction to help my principal induction, but I got something that was harder than the original.
P.S. I tried using the Physics forums android app, but I couldn't figure out how to post.
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