RMO 2014

Algebra Level 4

Let \(x_{1}, x_{2}, \ldots , x_{2014}\) be positive real numbers such that \(\displaystyle \sum_{j = 1}^{2014}x_{j} = 1\). Determine the smallest constant \(K\), such that \[K \displaystyle\sum_{j = 1} ^ {2014}
\dfrac{ x^2_{j} }{ 1 - x_{j} } \ge 1. \]


This problem is taken from RMO 2014.
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