RMO 2014

Algebra Level 4

Let x1,x2,,x2014x_{1}, x_{2}, \ldots , x_{2014} be positive real numbers such that j=12014xj=1\displaystyle \sum_{j = 1}^{2014}x_{j} = 1. Determine the smallest constant KK, such that Kj=12014xj21xj1.K \displaystyle\sum_{j = 1} ^ {2014} \dfrac{ x^2_{j} }{ 1 - x_{j} } \ge 1.


This problem is taken from RMO 2014.
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