# Prove that n^n (is less than or equal to) 1*3*5 .(2n-1).Where n is any natural no.

1. Feb 1, 2012

### Sumedh

Prove that n^n (is less than or equal to) 1*3*5.....(2n-1).Where n is any natural no.

1. The problem statement, all variables and given/known data
Prove that n^n (is less than or equal to) 1*3*5......(2n-1)

n^n ≥ 1*3*5......(2n-1)

.Where n is any natural number.I think Arithmetic or Geometric progression is used (A.P.>G.P.)

3. The attempt at a solution

i dont know how to solve this type of questions.
please give hints only for how to solve

2. Feb 1, 2012

### susskind_leon

Re: Prove that n^n (is less than or equal to) 1*3*5.....(2n-1).Where n is any natural

That seems to be a tricky problem.
I would suggest to try induction. Assume that the inequality holds for k. Then check what you multiply with on the left-hand side and on the right-hand side to get from k to (k+1). This way, I was able to show that what you multiply the left-hand side with is greater than that on the right-hand side, but it wasn't easy. Do the first steps and I can help you if you are having troubles.
btw: it's greater than or equal to, not less than or equal to

3. Feb 4, 2012

### Sumedh

Re: Prove that n^n (is less than or equal to) 1*3*5.....(2n-1).Where n is any natural

i got it