Let :
so the inequality is true.
Suppose the inequality is true for and prove for .
That means .
Using the statement for we have
Using the transitivity yelds the statement for .
I have to prove this inequality using mathematical induction:
(2)(4)(6).....(2n)
---------------- > 1 + (1/3) + (1/5) + .... + 1/(2n-1).
(1)(3)(5)....(2n-1)
I'm given that for positive reals a1, a2, a3,....,an where n >= 2 that
the cartesian product of (1 + ai) from i = 1 to n is greater than 1 + a1 + a2 + .... + an.
I know how to do the inductions with equal signs, but I can't seem to replace all the terms before (n + 1) on the left hand side with the terms on the right hand side (after assuming the statement is true for all n) since they're not equal.
How do you do this one?
Don't worry about the base case.
Thanks for any help.