Find the sum of first hundred even natural numbers divisible by 5.

If P(n) is the statement that the sum of first n natural numbers is divisible by n +1, prove that P(2r) is true for all r = 1, 2, 3,...... .

If P(n) is the statement “sum of first n natural numbers is divisible by n + 1", prove that P(r + 1) is true if P(r) is true.

Prove, by Principle of Mathematical Induction, that the sum of the cubes of three consecutive natural numbers is divisible by 9.

Find the mean of first five natural numbers.

Find the sum of first n natural numbers.

Find the sum of first 100 natural numbers.

Find the arithmetic mean of first ten even natural numbers.

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.