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Math Help - problem with an inequality

  1. #1
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    problem with an inequality

    I have seen a theorem:
    If a1,a2,........,an are n positive numbers such that all are not equal, and m is any rational number not equal to 1 and 0,
    then
    {(a1+a2+........+an)/n}m ≤ or ≥ {(a1m+a2m+........+anm)/n} according as m doesn't or does lie between 0 and 1


    I can't find out, when do they get equal?
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  2. #2
    MHF Contributor

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    Re: problem with an inequality

    Just off the top of my head, but since the change from \le to \ge, and vice-versa, occurs at 0 and 1, I would guess that the only places we could have "=" would be at 0 or 1 or both.
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