inequalities for differences of powers

Oftentimes, one needs to estimate differences of powers of real numbers. The following inequalitiesMathworldPlanetmath are useful for this purpose:


Here n is an integer greater than 1. The first inequality holds when 0<v<u, the second inequality holds when -1<x, and the third inequality holds when -1<x<1/(n-1). Equality can only occur in the latter two inequalities when x=0.

Title inequalities for differences of powers
Canonical name InequalitiesForDifferencesOfPowers
Date of creation 2013-03-22 15:48:42
Last modified on 2013-03-22 15:48:42
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 11
Author rspuzio (6075)
Entry type Theorem
Classification msc 26D99
Related topic BernoullisInequality