Prove that $\displaystyle \frac{1}{n}\left(1+\frac{1}{2}+\cdots+\frac{1}{n}\ right)\geq\sqrt[n]{n+1}-1$ where $\displaystyle n$ is a postive integer.

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- Apr 4th 2008, 12:36 PMmath sucksInequality Problem
Prove that $\displaystyle \frac{1}{n}\left(1+\frac{1}{2}+\cdots+\frac{1}{n}\ right)\geq\sqrt[n]{n+1}-1$ where $\displaystyle n$ is a postive integer.