MathDB

Classic polygon inequality

Source: ILL 1979 - Problem 63.

June 5, 2011

inequalitiestriangle inequalityinequalities proposed

Problem Statement

Let the sequence

\{a_i\}

n

positive reals denote the lengths of the sides of an arbitrary

n

-gon. Let

s=\sum_{i=1}^{n}{a_i}

. Prove that

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