Problem

Source: MOP 2005 Homework - Blue Group #7

Tags: inequalities, inequalities unsolved



Let n be a positive integer with n>1, and let a1, a2, ..., an be positive integers such that a1<a2<...<an and 1a1+1a2+...+1an1. Prove that (1a21+x2+1a22+x2+...+1a2n+x2)2121a1(a11)+x2 for all real numbers x.