Prove the following by using the principle of mathematical induction for all `n in N`:`n(n + 1) (n + 5)`is a multiple of 3.

Explanation

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


Let `P(n)=n(n+1)(n+5)=3 d` where `d in 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)=3 m` where `m in N`



`Rightarrow {k}^{3}+6 {k}^{2}+5 {k}=3 m`


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