Question

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

Answer 1

let n and n-1 be the 2 positive integers.
product = n(n-1)
= n2-n

CASE 1 (when n is even)
Let n = 2q
n2 - n = (2q)2-2q
= 4q2-2q
= 2q(2q-1)
Hence the product n2-n is divisible by 2

CASE 2(when n is odd)
Let n be 2q+1
n2 -n = (2q+1)2- (2q+1)
= 4q2+4q+1-2q-1
= 4q2+2q
= 2q(2q+1)

Hence the product n2-n is divisible by 2

hence the prooved...

hope this helps u...
Mark it as brainliest plz