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Find n so that inequality holds

Source: Baltic Way 2009

December 4, 2009
inequalitiesinequalities proposed

Problem Statement

Determine all integers n>1 n>1 for which the inequality x_1^2\plus{}x_2^2\plus{}\ldots\plus{}x_n^2\ge(x_1\plus{}x_2\plus{}\ldots\plus{}x_{n\minus{}1})x_n holds for all real x1,x2,…,xn x_1,x_2,\ldots,x_n.
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