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# inequalities for differences of powers

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

$n(u-v)v^{{n-1}}<u^{n}-v^{n}<n(u-v)u^{{n-1}}$ |

$nx\leq(1+x)^{n}-1$ |

$(1+x)^{n}-1\leq{nx\over 1-(n-1)x}$ |

Related:

BernoullisInequality

Type of Math Object:

Theorem

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

26D99*no label found*

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