If `P(n)` is the statement `n(n+1)(n+2)` is divisible is 12 prove that the statements `P(3)` and `P(4)` are true, but that `P(5)` is not true.

Explanation

Given, `P(n)=n(n+1)(n+2).`

Now,
i) `P(3)=3.4.5=60` is divisible by 12.

ii) `P(4)=4.5.6=120 `is divisible by 12.

iii) `P(5)=5.6.7=210` not divisible by 12.

iv)` P(8)=8.9.10=720 `is divisible by 12.

So `P(5) `is not true.