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An easy ineq; ISI BS 2011, P1

Source:

March 31, 2013

calculusinequalitiesrearrangement inequalityn-variable inequality

Problem Statement

Let

x_1, x_2, \cdots , x_n

be positive reals with

x_1+x_2+\cdots+x_n=1

. Then show that

\sum_{i=1}^n \frac{x_i}{2-x_i} \ge \frac{n}{2n-1}