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Prove x^n < n!

  1. Sep 21, 2009 #1
    proof xn < n!
     
  2. jcsd
  3. Sep 21, 2009 #2
    We would be happy to help you if you at least try the problem yourself and show us what you have tried
     
  4. Sep 21, 2009 #3

    Office_Shredder

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    Staff Emeritus
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    Obviously not.

    31>1!

    Have you started trying to prove it yet? Presumably the question asks to prove that for large enough n.... what are your initial thoughts?
     
  5. Sep 21, 2009 #4
    Maybe he means n^n<n! becuase there is always [tex]x=n!^{1\over n}[/tex] ?

    If so, you need to construct your argument around n^n = n*n*n*n...*n (n times) and n! = n(n-1)(n-2)...3.2.1 I think.
     
  6. Sep 21, 2009 #5

    Borek

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    Staff: Mentor

    Perhaps for n approaching infinity?
     
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