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2

Part of 1989 China National Olympiad

Problems(1)

China Mathematical Olympiad 1989 problem2

Source: China Mathematical Olympiad 1989 problem2

10/28/2013
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}}.
inequalities