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ILL 1967 Problem 47

    Prove the following inequality: ∏i=1kxi⋅∑i=1kxin−1≤∑i=1kxin+k−1,\prod^k_{i=1} x_i \cdot \sum^k_{i=1} x^{n-1}_i \leq \sum^k_{i=1} x^{n+k-1}_i, where xi>0,x_i > 0, k∈N,n∈N.k \in \mathbb{N}, n \in \mathbb{N}.

    Dataset text AoPS wiki problems. Quoted with source.

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