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Math Help - Proving an inequation with induction

  1. #1
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    Proving an inequation with induction

    Hi, I need help with this simple (I think) inequality:
    I need to prove with induction that for each natural number n the following inequation is true: (see the "small" image below)

    I tried to use the Latex system but I keep getting errors for some reason...

    Thanks in advance
    Attached Thumbnails Attached Thumbnails Proving an inequation with induction-limits.jpg  
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  2. #2
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    Re: Proving an inequation with induction

    The LaTeX code:
    [TEX]\left( {\frac{{n + 1}}{4}} \right)^n \leqslant n![/TEX]
    gives
    \left( {\frac{{n + 1}}{4}} \right)^n  \leqslant n!

    HINT:
    \left( {N + 1} \right)! = \left( {N + 1} \right)N! \geqslant \left( {\frac{{N + 1}}{4}} \right)\left( {\frac{{N + 1}}{4}} \right)^N
    Last edited by Plato; December 9th 2011 at 11:05 AM.
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  3. #3
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    Re: Proving an inequation with induction

    Thanks, I hope that this trick is going to help me.
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