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Math Help - INequality with powers

  1. #1
    Senior Member I-Think's Avatar
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    INequality with powers

    Need to solve

    (\frac{2011}{n+1})^{n+1}<(\frac{2011}{n})^n<br />
    Tried natural logs to get

    log_e{ }2011<n(log_e(n+1)-log_e{ }n)+log_e(n+1)<br />
    Stuck here

    Any ideas please?
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  2. #2
    Senior Member
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    Staten Island, NY
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    Perhaps cross multiply and cancel to get

    2011n^n<(n+1)^{n+1}.

    This can be put in the form

    2011<(\frac{n+1}{n})^n(n+1).

    The right hand side is approximately e(n+1) for large n.
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