If `g_1 and g_2` are two geometric means between a and b, prove that `g_1g_2 = ab`.

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

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

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

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

If g_1 , g_2 are two G.M's between two numbers a and b, then (g_1^2)/(g_2)+(g_2^2)/(g_1) is equal to:

Let alpha and beta be two positive real numbers. Suppose A_1, A_2 are two arithmetic means; G_1 ,G_2 are tow geometrie means and H_1 H_2 are two harmonic means between alpha and beta , then

If a,b,c are in G.P. and x,y are the arithmetic means of a,b and b,c respectively. Then prove that a/x+c/y=2 and 1/x+1/y=2/b .

What is the difference between g and G?