Find the Harmonic Mean(HM ) between 1 and `1/2`

Two AMs. A_1 and A_2 , two GMs. G_1 and G_2 and two HMs. H_1 and H_2 are inserted between any two numbers. Then find the arithmetic mean between H_1 and H_2 in terms of A_1, A_2, G_1, G_2 .

Find the 5th harmonic mean when n harmonic means are inserted between 1 and 2.

Statement -I: If H is the harmonic mean between a and b then (H+ a)/(H-a)+(H+ b)/(H- b)=1/2 Statement - II : If H is the harmonic mean between x and y then H=(2xy)/(x+y)

Statement-I: If H is the harmonic mean between a and b then (H+a)/(H-a)+(H+b)/(H-b)=(1)/(2) Statement -II: If H is the harmonic mean between x and y then H=(2xy)/(x+y)

If b is the harmonic mean between a and c, then prove that (1)/(b - a) + (1)/(b - c) = (1)/(a) + (1)/(c)

If b is the harmonic mean between a and c, then prove that (1)/(b - a) + (1)/(b - c) = (1)/(b) + (1)/(c)

If b is the harmonic mean between a and c, then prove that (1)/(b-a)+(1)/(b-c)=(1)/(a)+(1)/(c)

Find the mean proportion between 1 . 8 and 0.2