Let a1, a2, .... be positive real numbers in geometric progression. For each n,let An, Gn, Hn be respectively, the arithmetic mean, geometric mean, and harmonic mean of a1; a2, ...., an. Find an expression for the geometric mean of G1, G2,...,Gn in terms of A1, A2,..., An, H1, H2 ,..., Hn.
