MathDB

classic application of jensen

Source: bmo 1984

April 23, 2007

inequalitiesfunctionalgebran-variable inequalitycalculus

Problem Statement

Let

n \geq 2

be a positive integer and

a_{1},\ldots , a_{n}

be positive real numbers such that

a_{1}+...+a_{n}= 1

. Prove that:

\frac{a_{1}}{1+a_{2}+\cdots +a_{n}}+\cdots +\frac{a_{n}}{1+a_{1}+a_{2}+\cdots +a_{n-1}}\geq \frac{n}{2n-1}