Prove the following statement in Description below.

Question

Prove: The product of three consecutive integers is even.

Answer 1

THe product of an odd and an even is even: (2t)(2t+1) is divisible by 2.

Among N(N+1)(N+2) is at least one odd and one even.

THe product must be event...

Think of it this way, for integer t

The product looks like this (2t)(2t+1)(2t+2) = (4t)(2t+1)(t+2) which is divisible by 2

OR

The product looks like this (2t+1)(2t+2)(2t+3) = 2(2t+1)(t+1)(2t+3) which is also divisible by 2