MathDB
Bosnia and Herzegovina TST 2001 Day 2 Problem 2

Source: Bosnia and Herzegovina Team Selection Test 2001

September 19, 2018
inequalitiesalgebra

Problem Statement

Let nn be a positive integer, n≥1n \geq 1 and x1,x2,...,xnx_1,x_2,...,x_n positive real numbers such that x1+x2+...+xn=1x_1+x_2+...+x_n=1. Does the following inequality hold ∑i=1nxi1−x1⋅...⋅xi−1⋅xi+1⋅...xn≤11−(1n)n−1\sum_{i=1}^{n} {\frac{x_i}{1-x_1\cdot...\cdot x_{i-1} \cdot x_{i+1} \cdot ... x_n}} \leq \frac{1}{1-\left(\frac{1}{n}\right)^{n-1}}
Back to ProblemsView on AoPS