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x_1,...,x_n

Source: Iranian National Olympiad (3rd Round) 2006

September 19, 2006
inequalitiesinequalities proposed

Problem Statement

For positive numbers x1,x2,…,xsx_{1},x_{2},\dots,x_{s}, we know that ∏i=1sxk=1\prod_{i=1}^{s}x_{k}=1. Prove that for each m≥nm\geq n ∑k=1sxkm≥∑k=1sxkn\sum_{k=1}^{s}x_{k}^{m}\geq\sum_{k=1}^{s}x_{k}^{n}
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