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Math Help - Inequalities Q

  1. #1
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    Inequalities Q

    hey, can you guys give me a hand on this question:

    Prove \sqrt[n]{n!}<\sqrt[n+1]{(n+1)!}

    thanks
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  2. #2
    ynj
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    Quote Originally Posted by vuze88 View Post
    hey, can you guys give me a hand on this question:

    Prove \sqrt[n]{n!}<\sqrt[n+1]{(n+1)!}

    thanks
    \sqrt[n]{n!}<\sqrt[n+1]{(n+1)!}\Leftrightarrow\frac{\ln 1+...+\ln n}{n}<\frac{\ln 1+...+\ln n+1}{n+1} \Leftrightarrow \ln 1+...+\ln n<n\ln n+1.The last inequality is obvious.
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