Bernoulli’s inequality


Let x and r be real numbers. If  0>r>-1 or r>1 and x>-1 then

(1+x)r1+xr.

The inequalityMathworldPlanetmath also holds when r is an even integer. For 0<r<1 the inverse inequality holds.

Title Bernoulli’s inequality
Canonical name BernoullisInequality
Date of creation 2013-03-22 11:47:28
Last modified on 2013-03-22 11:47:28
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 12
Author rspuzio (6075)
Entry type Theorem
Classification msc 26D99
Classification msc 55R40
Classification msc 55U15
Classification msc 55T25
Classification msc 55M05
Classification msc 55U30
Classification msc 55U10
Related topic InequalitiesForDifferencesAndQuotientsOfPowers