For principle of mathematical induction to be true, what type of number should ‘n’ be?

72n + 22n – 2 . 3n – 1 is divisible by 50 by principle of mathematical induction.

By principle of mathematical induction, 24n-1 is divisible by which of the following?

If 103n + 24k + 1. 9 + k, is divisible by 11, then what is the least positive value of k?

P(n) = n(n2 – 1). Which of the following does not divide P(k+1)?

For any natural number n, 22n – 1 is divisible by

For all n ∈ N, 3.52n+1 + 23n+1 is divisible by

If n is an odd positive integer, then an + bn is divisible by :

If xn – 1 is divisible by x – k, then the least positive integral value of k is,

1

2

3

4

The sum of the series 1² + 2² + 3² + ………..n² is,

n(n + 1)(2n + 1)

n(n + 1)(2n + 1)/2

n(n + 1)(2n + 1)/3

n(n + 1)(2n + 1)/6

1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)} equals to

n(n + 1)

n/(n + 1)

2n/(n + 1)

3n/(n + 1)