MathDB

making the product to the fraction and reversing the sign

Source: ROMANIA 1999

July 15, 2005

inequalitiesinequalities proposed

Problem Statement

let

x_i,y_i 1 \le i \le n

be positive numbers such that :

\displaystyle \sum_{i=1}^n x_i \ge \sum_{i=1}^n x_iy_i

Prove :

\displaystyle \sum_{i=1}^n x_i \le \sum _{i=1}^n \frac{x_i}{y_i}