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This sum is always positive

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April 19, 2013
inequalities

Problem Statement

Prove that, for any real numbers a1,a2,…,ana_1, a_2, \dots , a_n, ∑i,j=1naiaji+j−1≥0. \sum_{i,j=1}^n \frac{a_ia_j}{i+j-1}\ge 0.
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