Harmonic mean

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of numbers $a_1,\dots,a_n$

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


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

How to Cite This Entry:
Harmonic mean. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article