Harmonic mean

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.