MathDB

A2

Part of 2011 Balkan MO Shortlist

Problems(1)

maximum value of product of non-negative real numbers

Source: Balkan MO ShortList 2011 A2

4/6/2020
Given an integer n≥3n \geq 3, determine the maximum value of product of nn non-negative real numbers x1,x2,…,xnx_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*}