Question

1. Prove that the product of two consecutive positive integers is divisible by 2.
​

Answer 1

Answer:

Hence any integer is of one of the form 2q, 2q+1. Hence n(n+1) = 2((2q+1)(q+1)), which is even. Hence n(n+1) is always even. Hence the product of two consecutive integers is always divisible by 2.