If G is the gemetric mean between a and b, show that `1/(G+a) + 1/(G+b) = 1/G`

If G_1 is the first of n geometric means between a and b, show that : G_1^(n+1) =a^n b .

What is the difference between g and G?

If G is the geometric mean between two distinct positive numbers a and b, then show that 1/(G-a)+1/(G-b)=1/G .

If m is the A.M. of two distinct real numbers l and n""(""l ,""n"">""1) and G1, G2 and G3 are three geometric means between l and n, then G1 ^4+2G2 ^4+G3^ 4 equals, (1) 4l^2 mn (2) 4l^m^2 mn (3) 4l m n^2 (4) 4l^2m^2n^2

Establish the relation between 'g' and 'G' .

State the relation between 'g' and 'G'?

If a is the A.M. of b and c and the two geometric means are G_(1) and G_(2) , then prove that G_(1)^(3)+G_(2)^(3) = 2abc

Let A_(1),A_(2),A_(3),"......."A_(m) be arithmetic means between -3 and 828 and G_(1),G_(2),G_(3),"......."G_(n) be geometric means between 1 and 2187. Product of geometric means is 3^(35) and sum of arithmetic means is 14025. The value of n is