If p is the first of the n arithmetic means between two numbers and q be the first on n harmonic means between the same numbers. Then, show that q does not lie between p and `((n+1)/(n-1))^2 p.`

If p be the first of n arithmetic means between two numbers and q be the first of n harmonic means between the same two numbers , then prove that the value of q can not lie between p and ((n+1)/(n-1))^2p .

If A be the arithmetic mean between two numbers and S be the sum of n arithmetic means between the same numbers, then -

Insertion of n arithmetic means between two terms

Let p( gt 0) be the first of the n arthimatic means betweens between two numbers and q( gt 0) the first of n harmonic means between the same numbers. Then prove that qnotin(p,((n+1)/(n-1))^(2)p)andpnotin(((n-1)/(n+1))^(2)q,q)

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 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 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 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 p is