Find n such that `(a^n+b^n)/(a^(n-1)+b^(n-1))` may be the geometric mean between two quantities a and b.

Find the value of n so that (a^(n+1)+ b^(n+1))/(a^n+b^n) may be the geometric mean between a and b.

Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n) may be the geometric mean between a and b .

Find n, so that (a^(n+1)+b^(n+1))/(a^(n)+b^(n))(a ne b ) be HM beween a and b.

If (a^n+b^n)/(a^(n-1)+b^(n-1)) is the A.M. between a and b, then find the value of n.

Suppose p is the first of n(ngt1) arithmetic means between two positive numbers a and b and q the first of n harmonic means between the same two numbers. The value of p is

Suppose p is the first of n(ngt1) arithmetic means between two positive numbers a and b and q the first of n harmonic means between the same two numbers. The value of q is

Find the derivative of (ax + b)^n

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

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)) .

Let P(n) be the statement : “the arithmetic mean of n and (n + 2) is the same as their geometric mean”’. Prove that P(1) is not true. Also prove that if P(n) is true, then P(n + 1) is also true. How does this contradict the principle of Induction ?