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Math Help - Inequality

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    6

    Inequality

    Hey

    For A Sequence
    a_n=n^{\frac{1}{n}}-1
    Where a_n>0,n>1

    How Can I Deduce That
    \forall n>1,n-1\geq\frac{1}{2}n\left(n-1\right)a_n^2
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  2. #2
    Member
    Joined
    Mar 2009
    Posts
    91
    Rearrange as n=(1+a_n)^n and binomial expansion n=1+na_n+\frac{n(n-1)}2a_n^2+\dots>1+\frac{n(n-1)}2a_n^2 does the trick.
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