MathDB
Indian RMO- Paper 2

Source: Problem 5

December 11, 2013
limitinequalities

Problem Statement

Let n≥3n \ge 3 be a natural number and let PP be a polygon with nn sides. Let a1,a2,⋯ ,ana_1,a_2,\cdots, a_n be the lengths of sides of PP and let pp be its perimeter. Prove that a1p−a1+a2p−a2+⋯+anp−an<2\frac{a_1}{p-a_1}+\frac{a_2}{p-a_2}+\cdots + \frac{a_n}{p-a_n} < 2
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