Prove that for all n in the naturals, n(n+1)(n+2) is divisible by 3

By induction:

It's true for , since clearly contains a factor of 3.

Suppose it's true for , that is divisible by 3. Then



where is an integer. This reduces to



and both terms are clearly multiples of 3. We know that is an integer since we had set previously, which implies is a multiple of . So the statement is true.

Ais the correct answer

This is too long-standing now get out