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Sum of product

Source: APMO 1990

March 11, 2006
LaTeXalgebrapolynomialinequalities unsolvedinequalities

Problem Statement

Let a1a_1, a2a_2, ⋯\cdots, ana_n be positive real numbers, and let SkS_k be the sum of the products of a1a_1, a2a_2, ⋯\cdots, ana_n taken kk at a time. Show that SkSn−k≥(nk)2a1a2⋯an S_k S_{n-k} \geq {n \choose k}^2 a_1 a_2 \cdots a_n for k=1k = 1, 22, ⋯\cdots, n−1n - 1.
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