Difference between revisions of "Harmonic mean"
From Encyclopedia of Mathematics
(Importing text file) |
(TeX) |
||
| Line 1: | Line 1: | ||
| − | ''of numbers | + | {{TEX|done}} |
| + | ''of numbers $a_1,\ldots,a_n$'' | ||
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 | ||
| − | + | $$\frac{n}{\frac{1}{a_1}+\ldots+\frac{1}{a_n}}.$$ | |
| − | Thus, | + | 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. |
Revision as of 13:10, 9 April 2014
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://encyclopediaofmath.org/index.php?title=Harmonic_mean&oldid=17187
Harmonic mean. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Harmonic_mean&oldid=17187
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article