hey, can you guys give me a hand on this question: Prove $\displaystyle \sqrt[n]{n!}<\sqrt[n+1]{(n+1)!}$ thanks
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Originally Posted by vuze88 hey, can you guys give me a hand on this question: Prove $\displaystyle \sqrt[n]{n!}<\sqrt[n+1]{(n+1)!}$ thanks $\displaystyle \sqrt[n]{n!}<\sqrt[n+1]{(n+1)!}\Leftrightarrow\frac{\ln 1+...+\ln n}{n}<\frac{\ln 1+...+\ln n+1}{n+1}$$\displaystyle \Leftrightarrow \ln 1+...+\ln n<n\ln n+1$.The last inequality is obvious.
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