MathDB

2a

Part of 1999 Romania National Olympiad

Problems(1)

making the product to the fraction and reversing the sign

Source: ROMANIA 1999

7/15/2005
let xi,yi1≤i≤nx_i,y_i 1 \le i \le n be positive numbers such that : ∑i=1nxi≥∑i=1nxiyi\displaystyle \sum_{i=1}^n x_i \ge \sum_{i=1}^n x_iy_i Prove : ∑i=1nxi≤∑i=1nxiyi\displaystyle \sum_{i=1}^n x_i \le \sum _{i=1}^n \frac{x_i}{y_i}
inequalitiesinequalities proposed