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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 #1
    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. jcsd
  3. Feb 1, 2012 #2
    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
     
  4. Feb 4, 2012 #3
    Re: Prove that n^n (is less than or equal to) 1*3*5.....(2n-1).Where n is any natural

    i got it
    thank you for your help
     
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