prove that

To prove: Product of any two positive consecutive integer is divisible by 2

Proof: Since the two number are consecutive. So one of them should be even.

Let the two numbers be 2x and 2x+1

Product of the two numbers = 2x (2x+1)

                                                   = 2(x² +1), which is divisible by 2.

Hence Proved.

This result can also be proved by mathematical induction.