MathDB
China Mathematical Olympiad 1989 problem2

Source: China Mathematical Olympiad 1989 problem2

October 28, 2013
inequalities

Problem Statement

Let x1,x2,…,xnx_1, x_2, \dots ,x_n (n≥2n\ge 2) be positive real numbers satisfying ∑i=1nxi=1\sum^{n}_{i=1}x_i=1. Prove that:∑i=1nxi1−xi≥∑i=1nxin−1.\sum^{n}_{i=1}\dfrac{x_i}{\sqrt{1-x_i}}\ge \dfrac{\sum_{i=1}^{n}\sqrt{x_i}}{\sqrt{n-1}}.
Back to ProblemsView on AoPS