Prove the following:
(1x3x5x...x(2n-1))/(2x4x6x...x(2n)) <= 1/(2n+1)^.5
The Attempt at a Solution
1) Following the general steps of proof by induction, I first proved that the statement is true for the case n=1.
2) Next, I substituted n+1 for n into the equation.
3) Using algebra, I have hammered away at the problem from every angle that I can think of in hopes to end up with the same formula as in the original case. Is this the correct way to go about solving this problem? My best attempt thus far is in the attached file. My work begins with my substitution of n+1 for n.