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