Question

Let P(n) is the statement the product of two consecutive natural numbers is even. Then which of the following is true?

• A. P(20)
• B. P(3)
• C. P(100)
• D. P(n), n Є N

Answer 1

The correct option is D

P(n), n Є N

P(1) = 1(1 + 1) = 2 (even)

Let P(k) = k( k + 1) = 2q , where q is a positive integer .

P(k + 1) = (k + 1) (k + 2) = k(k + 1) +2(k + 1)

= 2q + 2(k + 1) = 2 (q + k + 1) = (even)

Hence, by principle of mathematical induction the statement P(n) is true for all natural numbers.