Prove that the sum of n arithmatic means between two numbers is n times the single A.M. between them.

Insert 6 arithmatic mean between 3 and 24.

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.

Prove that the sum of two odd numbers is even.

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

Form the pair of linear equations for the problems and find their solution by substitution method: The difference between two numbers is 26 and one number is three times the other. Find them.

In a right angle triangle, the sum of hypotenuous and one side is given, Prove that when the angle between them is (pi)/(3) , the area of the triangle is maximum.

Statement 1 The difference between the sum of the first 100 even natural numbers and the sum of the first 100 odd natural numbers is 100. Statement 2 The difference between the sum opf the first n even natural numbers and sum of the first n odd natural numbers is n.

If the mean of first n natural numbers is (5n)/(9) , then find n

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)) .