it is the arithmetic mean of the recipricals of the data values.
It is used for a number of purposes in maths, but one example
is: if you complete a journey of N 1 mile stages with speed v_n
on the n-th stage, then the average speed for the whole journey is:
As a<b, 1/a>1/b, so: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.
(1/h) = (1/2)((1/a)+(1/b)) <(1/2)((1/a) + (1/a))=1/a
(1/h) = (1/2)((1/a)+(1/b)) >(1/2)((1/b) + (1/b))=1/b