- #1
cupcakes
- 18
- 0
Homework Statement
[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.
Homework Equations
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.
Last edited: