using mathematical induction prove that n(n+1)(n+2) is divisible by 6.

Let the given statement be P(n) i.e.,

For n = 1, we have

Let P(k) be true for some positive integer k, i.e.

We shall now prove that P(k + 1) is true.

∴ P(k) is true ⇒ P(k + 1) is true.

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