# Bernoulli’s inequality

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

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

The inequality also holds when $r$ is an even integer. For $0 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