Harmonic Progressions

The terms of a series are in harmonic progression if the reciprocals of the terms are in arithmetic progression.


To know what are arithmetic progression please read Arithmetic Progression
            

Terms a, b and c are in harmonic progression if 1/a. 1/b and 1/c are in arithmetic progression.

Relation between the A.M., G.M. and H.M.

Let a nd b are any two numbers then

     1.    A.M. > G.M. > H.M.

    (a+b)/2 > √ab > 2ab/(a+b)

      2.    A.M., G.M. and H.M. are in geometric progression.

           G.M^{. 2} = ab = {(a+b)/2 } x {2ab/(a+b)|  = (A.M.) x (H.M.)