I have proven to n=3 an inequality that seems useful. x(adsbygoogle = window.adsbygoogle || []).push({}); _{1}^{n}+...+x_{n}^{n}≥nx_{1}...x_{n}for all positive x.

I'm sure this has been proven before. I'm not quite sure how to extend it from n=3 to for all n. I'm thinking induction, but that has proven challenging. Any hints?

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# A conjecture

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