What exactly is meant by the term HARMONIC MEAN?

I think of the word harmonic in terms of music but not in terms of mathematics.

QUESTION:

For 0 < a < b, let h be defined by

(1/h) = (1/2)((1/a)+(1/b)).

Show that a < h < b. The number h is called the harmonic mean of a and b.

Also, is there another purpose for the harmonic mean other than just proving the above?