Let `h_(n)` and `g_(n)` be harmonic and geometric sequences respectively. If `h_(1)` = `g_(1)` = `1/2` and `h_(10)` = `g_(10)` =`(1)/(1024)` then

Lef a, b be two distinct positive numbers and A and G their arithmetic and geometric means respectively. If a, G_(1),G_(2) , b are in G.P. and a, H_(1),H_(2) , b are in H.P., prove that (G_(1)G_(2))/(H_(1)H_(2))lt (A^(2))/(G^(2)) .

Let a_(1),a_(2),a_(3),......,a_(m) be the arithmetic means between -2 and 1027 and let g_(1),g_(2),...,g_(n) be the geometric mean between 1 and 1024.g_(1)*g_(2)*g_(3)...g_(n)=2^(45) and a_(1)+a_(2)+a_(3)+....+a_(m)=1025xx171 (i) The value of n is : (ii) The value of m is

If n_(1) and n_(2) are the sizes, G_(1) and G_(2) the geometric means of two series respectively, then which one of the following expresses the geometric mean (G) of the combined series?