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

[Sumedh]

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

Homework Statement

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.)

The Attempt at a Solution

i don't know how to solve this type of questions.
please give hints only for how to solve

 

[susskind_leon]

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

 

[Sumedh]

i got it
thank you for your help