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Harmonic mean

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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