n / (n-1)^k
Source: IMO Longlist 1989, Problem 61
September 18, 2008
inequalitiescalculusderivativefunctioninequalities unsolved
Problem Statement
Prove for and a_i \in \mathbb{R}^\plus{}, i \equal{} 1,2 \ldots, n the following inequality holds:
\left( \frac{a_1}{a_2 \plus{} \ldots \plus{} a_n} \right)^k \plus{} \ldots \plus{} \left( \frac{a_n}{a_1 \plus{} \ldots \plus{} a_{n\minus{}1}} \right)^k \geq \frac{n}{(n\minus{}1)^k}.