# Harmonic mean

From Encyclopedia of Mathematics

*of numbers $a_1,\ldots,a_n$*

The number reciprocal to the arithmetic mean of the reciprocals of the given numbers, i.e. the number

$$\frac{n}{\frac{1}{a_1}+\ldots+\frac{1}{a_n}}.$$

Thus, $1/n$ is the harmonic mean of the fractions $1/(n-1)$ and $1/(n+1)$, $n=2,3,\ldots$. The harmonic mean of given numbers is never greater than their arithmetic mean.

**How to Cite This Entry:**

Harmonic mean.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Harmonic_mean&oldid=31436

This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article