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Source: Romanian Nationals RMO 2005 - grade 9, problem 4

March 31, 2005
geometryinequalitiesinequalities proposedn-variable inequality

Problem Statement

Let x1,x2,…,xnx_1,x_2,\ldots,x_n be positive reals. Prove that 11+x1+11+x1+x2+⋯+11+x1+⋯+xn<1x1+1x2+⋯+1xn. \frac 1{1+x_1} + \frac 1{1+x_1+x_2} + \cdots + \frac 1{1+x_1+\cdots + x_n} < \sqrt { \frac 1{x_1} + \frac 1{x_2} + \cdots + \frac 1{x_n}} . Bogdan Enescu
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