MathDB
y_1\le y_2\le...\le y_n, such that x_k \le y_k \le 2x_k for all k=1,2,..., n

Source: St. Petersburg 2016 10.2

May 1, 2019
algebrainequalitiespositive real

Problem Statement

Given the positive numbers x1,x2,...,xnx_1, x_2,..., x_n, such that xi≤2xjx_i \le 2x_j with 1≤i<j≤n1 \le i < j \le n. Prove that there are positive numbers y1≤y2≤...≤yny_1\le y_2\le...\le y_n, such that xk≤yk≤2xkx_k \le y_k \le 2x_k for all k=1,2,...,nk=1,2,..., n
Back to ProblemsView on AoPS