MathDB
min max of x_1^2+x_2^2+...+x_n^2 if x_1+ 2x_2 + ... + nx_n = 1

Source: Rioplatense 1998 L3 P2

September 19, 2022
algebrainequalitiesminmax

Problem Statement

Given an integer n>2n > 2, consider all sequences x1,x2,...,xnx_1,x_2,...,x_n of nonnegative real numbers such that x1+2x2+...+nxn=1.x_1+ 2x_2 + ... + nx_n = 1. Find the maximum value and the minimum value of x12+x22+...+xn2x_1^2+x_2^2+...+x_n^2 and determine all the sequences x1,x2,...,xnx_1,x_2,...,x_n for which these values are obtained.
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