Principal of mathematical induction

Q1. n(n+1)(n+5) is a multiple of 3.

Proof:-

 We will prove it by using the formula of mathematical induction for all n ϵ N

Let P(n)=n(n+1)(n+5)=3d where d ϵ N

For n=1

P(1)=1(2)(6)=12 which is divisible by 3

Let P(k) is true 

P(k)=k(k+1)(k+5)=3m where m ϵ N

Since P(k+1) is true whenever P(k) is true.

So, by the principle of induction, P(n) is divisible by 3 for all n ϵ N