MathDB

4

Part of 2004 Singapore MO Open

Problems(1)

sum x_i/(1+(n-1)x_i) <=1 where 0 < ,x_i <= 1

Source: Singapore Open Math Olympiad 2004 2nd Round p4 SMO

4/3/2020
If 0<x1,x2,...,xn≤10 <x_1,x_2,...,x_n\le 1, where n≥1n \ge 1, show that x11+(n−1)x1+x21+(n−1)x2+...+xn1+(n−1)xn≤1\frac{x_1}{1+(n-1)x_1}+\frac{x_2}{1+(n-1)x_2}+...+\frac{x_n}{1+(n-1)x_n}\le 1
inequalitiesalgebra