TOPICS
Search

Arithmetic-Harmonic Mean

Let

a_(n+1)=1/2(a_n+b_n)
(1)
b_(n+1)=(2a_nb_n)/(a_n+b_n).
(2)

Then

A(a_0,b_0)=lim_(n->infty)a_n=lim_(n->infty)b_n=sqrt(a_0b_0),
(3)

which is just the geometric mean.

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Arithmetic-Harmonic Mean." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Arithmetic-HarmonicMean.html

Subject classifications