Question

can someone help me with the solution plz..

Answer 1

$\textsf{Let x_1,x_2,......,x_{2014} be real positive numbers such that } \displaystyle \sum_{j=1}^{2014} x_j = 1. \\\\\textsf{Determine with proof the smallest constant K such that:}\\\\ K \sum^{2014}_{j=1} \dfrac{x^2_j}{1-x_j} \geq 1.$