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# 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 $0<r<1$ the inverse inequality holds.

Related:

InequalitiesForDifferencesAndQuotientsOfPowers

Type of Math Object:

Theorem

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

26D99*no label found*55R40

*no label found*55U15

*no label found*55T25

*no label found*55M05

*no label found*55U30

*no label found*55U10

*no label found*

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