Question: n(n+1)(n+5) is a multiple of 3?
Answer: Answer. Let P(n): n(n + 1)(n + 5) is a multiple of 3. For n = 1, the given expression becomes (1 × 2 × 6) = 12, which is a multiple of 3. ... Hence, by the principle of mathematical induction, P(n) is true for all n ∈ N.