MathDB

Power colombian inequality

Source: IberoAmerican Olympiad For University Students

July 10, 2011

inequalitiesinductioninequalities proposed

Problem Statement

Prove that for all positive integers

n

and for all real numbers

x

such that

0\le x\le1

, the following inequality holds:

\left(1-x+\frac{x^2}{2}\right)^n-(1-x)^n\le\frac{x}{2}