MathDB

[2019] Ordered Inequality of an Odd nr. of Variables

Source:

December 16, 2019

inequalitiesn-variable inequality

Problem Statement

Let be an odd natural number

n,

and

n

real numbers

y_1\le y_2\le\cdots\le y_n

whose sum is

0.

Prove that

(n+2)y_{\frac{n+1}{2}}^2\le y_1^2+y_2^2+\cdots +y_n^2,

and specify where equality is attained.
Nicolae Bourbăcuț