Question

Prove that the following by using the Priniciple of mathematical Induction for all nE N: n(n+1)(n+5) is a multiple of 3.​

Answer 1

Answer:

True

Step-by-step explanation:

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. So, the given statement is true for n = 1, i.e. P(1) is true. ... Hence, by the principle of mathematical induction, P(n) is true for all n ∈ N.