MathDB
TOT 118 1986 Spring S6 a^2_1-a^2_2+ ...+a^2_{2n- l} \ge (a_1- ...+a_{2n- l})^2

Source:

August 29, 2019
algebrainequalities

Problem Statement

Given the nonincreasing sequence of non-negative numbers in which a1≥a2≥a3≥...≥a2n−1≥0a_1 \ge a_2 \ge a_3 \ge ... \ge a_{2n-1}\ge 0.
Prove that a12−a22+a32−...+a2n−l2≥(a1−a2+a3−...+a2n−l)2a^2_1 -a^2_2 + a^2_3 - ... + a^2_{2n- l} \ge (a_1 - a_2 + a_3 - ... + a_{2n- l} )^2 .
( L . Kurlyandchik , Leningrad )
Back to ProblemsView on AoPS