困难的不等式

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若 $x_1，x_2,...,x_{n+1}>0$ 满足 $x_1x_2…x_{n+1}=1$
求证$\displaystyle \sum^{n+1}_{i=1}{n^{\frac 1{x_i}}}\geq\sum^{n+1}_{i=1}n^{\frac {x_i}{n}}$