MathDB

maximum value of product of non-negative real numbers

Source: Balkan MO ShortList 2011 A2

April 6, 2020

Problem Statement

Given an integer

n \geq 3

, determine the maximum value of product of

n

non-negative real numbers

x_1,x_2, \ldots , x_n

when subjected to the condition \begin{align*} \sum_{k=1}^n \frac{x_k}{1+x_k} =1 \end{align*}