MathDB

it's quite hard for me to characterize this..

Source: Moldova 2007 IMO-BMO TST III problem 1

March 24, 2007

inequalitiesinequalities proposed

Problem Statement

Let

a_{1}, a_{2}, \ldots, a_{n}\in [0;1]

. If

S=a_{1}^{3}+a_{2}^{3}+\ldots+a_{n}^{3}

then prove that

\frac{a_{1}}{2n+1+S-a_{1}^{3}}+\frac{a_{2}}{2n+1+S-a_{2}^{3}}+\ldots+\frac{a_{n}}{2n+1+S-a_{n}^{3}}\leq \frac{1}{3}