Question

Q. Prove that the product of two consecutive positive integer is divisible by 2.

Answer 1

Let the 2 consecutive numbers be, $x,x+1$

Product of these consecutive numbers=$x(x+1)$

Let, $x=2k$

product$=2k(2k+1)$

From above equation it is clear that the product is divisible by 2.

Let,$x=2k+1$

product$=(2k+1)\left[\right(2k+1)+1]$

$=2(2k^2+3k+1)$

From above equation it is clear that the product is divisible by 2.