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Indian RMO 2014 P6

Source:

December 7, 2014
inequalities

Problem Statement

Let x1,x2,x3…x2014x_1,x_2,x_3 \ldots x_{2014} be positive real numbers such that ∑j=12014xj=1\sum_{j=1}^{2014} x_j=1. Determine with proof the smallest constant KK such that K∑j=12014xj21−xj≥1K\sum_{j=1}^{2014}\frac{x_j^2}{1-x_j} \ge 1
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