The value of n for which ` (x^(n+1)+y^(n+1))/(x^(n)+y^(n))` is the geometric mean of x nd y is

Insert : Let (x^(n+1) + y^(n+1))/(x^(n) + y^(n)) be the geometric mean of x and y , find n.

If the arithmetic mean of x and y be (x^(n+1)+ y^(n+1))/(x^(n) + y^(n)) , then find n.

The geometric mean of (x _(1) , x _(2), x _(3), ... X _(n)) is X and the geometric mean of (y _(1), y _(2), y _(3),... Y _(n)) is Y. Which of the following is/are correct ? 1. The geometric mean of (x _(1) y _(1), x _(2) y _(2) . x _(3) y _(3), ... x _(n) y _(n)) is XY. 2. The geometric mean of ((x _(1))/( y _(1)) , ( x _(2))/( y _(2)), (x _(3))/( y _(3)) , ... (x _(n))/( y _(n))) is (X)/(Y). Select the correct answer using the code given below:

Compute the product : (x^n -y^(-n))(x^n +y^(-n)) .

(x^(2^n)-y^(2^n))/(x^(2^(n-1))+y^(2^(n-1)))=

Let G_(1),G_(2) be the geometric means of two series x_(1),x_(2),...,x_(n);y_(1),y_(2),...,y_(n). If G is the geometric mean of (x_(i))/(y_(i)),i=1,2,...n, then G is equal to