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SMO 2004 Problem 4

    If 0<x1,x2,...,xn≤10 <x_1,x_2,...,x_n\le 1 , where n≥1n \ge 1 , show that x11+(n−1)x1+x21+(n−1)x2+...+xn1+(n−1)xn≤1\frac{x_1}{1+(n-1)x_1}+\frac{x_2}{1+(n-1)x_2}+...+\frac{x_n}{1+(n-1)x_n}\le 1

    Dataset text AI-MO AoPS. Quoted with source.

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