Problem 412 (difficulty: 3/10)

Prove that if \(\displaystyle a_{1},...,a_{n}\geq 0\) and \(\displaystyle k>1\) is an integer, then \(\displaystyle \frac{a_{1}+...+a_{n}}{n}\leq \sqrt[k]{\frac{a_{1}^{k}+...+a_{n}^{k}}{n}}\).

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