Two A.M's `A_(1)` and `A_(2)`, two G.M's `G_(1)` and `G_(2)` and two H.M's `H_(1)` and `H_(2)` are inserted between two numbers `a` and `b`.
(i) Express `A_(1) + A_(2)` in terms of `a` and `b`.
(ii) Express `G_(1) G_(2)` in terms of `a` and `b`.
(iii) Express `1/H_(1) + 1/H_(2)1` in terms of `a` and `b`.
(iv) Show that `1/H_(1) + 1/h_(2) = (A_(1) + A_(2))/(G_(1) G_(2))`

Answer

(i) ` = a + b` (ii) `ab` (iii) ` = (a + b)/(ab)` (iv) ` (A_(1) + A_(2))/(G_(1) G_(2))`(from (i) and (ii))