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 A and G are the A.M. and G.M. respectively between any two distinct positive numbers a and b then show that A > G.

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

Let A_(1),G_(1),H_(1) denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For nge2 , let A_(n-1),G_(n-1)" and "H_(n-1) has arithmetic,geometric and harmonic means as A_(n),G_(n),H_(n) respectively. Which of the following statement is correct?

Let A_1 , G_1, H_1 denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For n >2, let A_(n-1),G_(n-1) and H_(n-1) has arithmetic, geometric and harmonic means as A_n, G_N, H_N, respectively a. A_(1)gtA_(2)gtA_(3)gt"......." b. A_(1)ltA_(2)ltA_(3)lt"......." c. A_(1)gtA_(3)gtA_(5)gt"......."" and " A_(2)ltA_(4)ltA_(6)lt"......." d. A_(1)ltA_(3)ltA_(5)lt"......."" and " A_(2)gtA_(4)gtA_(6)gt"......."

Let A_(1),G_(1),H_(1) denote the arithmetic, geometric and harmonic means respectively, of two distinct positive numbers. For nge2 , let A_(n-1),G_(n-1)" and "H_(n-1) has arithmetic,geometric and harmonic means as A_(n),G_(n),H_(n) respectively. Which of the following statement is correct? a. H_(1)gtH_(2)gtH_(3)gt"......." b. H_(1)ltH_(2)ltH_(3)lt"......." c. H_(1)gtH_(3)gtH_(5)gt"......." " and " H_(2)ltH_(4)ltH_(6)lt"......." d. H_(1)ltH_(3)ltH_(5)lt"......."" and " H_(2)gtH_(4)gtH_(6)gt"......."

What is the difference between g and G?

The A.M. between two positive numbers is 34 and their G.M. is 16. find the numbers.

If the geometric mea is (1)/(n) times the harmonic mean between two numbers, then show that the ratio of the two numbers is 1+sqrt(1-n^(2)):1-sqrt(1-n^(2)) .