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Induction problem

  1. Feb 3, 2004 #1
    I know I have to prove this using induction, but am having some problems.

    show n! > n^2 for all n >= 4

    what I have so far

    1) n=4; 4^2=16 < 4! = 4*3*2*1=24; 16 < 24

    2) show (n+1)! > (n+1)^2


    something a long the lines of..

    (n+1)! = (n+1)*n!
    > (n+1)*n^2
    .. then what, can I just say (n+1)n^2 > (n+1)^2? or am I missing a step or 2..


    thanks
     
    Last edited: Feb 3, 2004
  2. jcsd
  3. Feb 3, 2004 #2

    matt grime

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    Science Advisor
    Homework Helper

    well, you must prove that

    n^2(n+1) > (n+1)^2

    for n > 4.

    Thinking what happesn if we divide through by n+1, this it suffices to show n^2 > n+1

    which is clearly true for n>1, check the original statement is true for n=4 and you are done.
     
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