Difference between revisions of "Harmonic mean"
From Encyclopedia of Mathematics
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| − | ''of numbers $a_1,\ | + | ''of numbers $a_1,\dots,a_n$'' |
The number reciprocal to the [[Arithmetic mean|arithmetic mean]] of the reciprocals of the given numbers, i.e. the number | The number reciprocal to the [[Arithmetic mean|arithmetic mean]] of the reciprocals of the given numbers, i.e. the number | ||
| − | $$\frac{n}{\frac{1}{a_1}+\ | + | $$\frac{n}{\frac{1}{a_1}+\dots+\frac{1}{a_n}}.$$ |
| − | Thus, $1/n$ is the harmonic mean of the fractions $1/(n-1)$ and $1/(n+1)$, $n=2,3,\ | + | Thus, $1/n$ is the harmonic mean of the fractions $1/(n-1)$ and $1/(n+1)$, $n=2,3,\dots$. The harmonic mean of given numbers is never greater than their arithmetic mean. |
Latest revision as of 13:55, 30 December 2018
of numbers $a_1,\dots,a_n$
The number reciprocal to the arithmetic mean of the reciprocals of the given numbers, i.e. the number
$$\frac{n}{\frac{1}{a_1}+\dots+\frac{1}{a_n}}.$$
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: http://encyclopediaofmath.org/index.php?title=Harmonic_mean&oldid=31436
Harmonic mean. Encyclopedia of Mathematics. URL: http://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