MathDB
KJMO 2005 n-variable inequality

Source: KJMO 2005 p7

May 1, 2019
algebrainequalitiesInequalityn-variable inequality

Problem Statement

If positive reals x1,x2,⋯ ,xn x_1,x_2,\cdots,x_n satisfy ∑i=1nxi=1.\sum_{i=1}^{n}x_i=1. Prove that∑i=1n11+∑j=1ixj<23∑i=1n1xi\sum_{i=1}^{n}\frac{1}{1+\sum_{j=1}^{i}x_j}<\sqrt{\frac{2}{3}\sum_{i=1}^{n}\frac{1}{x_i}}
Back to ProblemsView on AoPS