Bernoulli’s inequality

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

$${(1+x)}^r\ge 1+xr.$$

The inequality also holds when $r$ is an even integer. For 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