# 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. \]