Question

The product of 2 consecutive numbers is divisible by 2 explain

Answer 1

HERE IS THE SOLUTION;

◆ Let u consider two consecutive +ve integer as n and another as n-1.

Now, the product of both is n2-n

Case 1

When n=2q ( Since any +ve integer can be in the form of 2q or 2q+1)

n2-n= (2q)2-2q

  = 4q2- 2q

It is divisible by 2 as it leaves a remainder 0 after division.

Case 2

When n= 2q+1

n2-n = (2q+1)2 - 2q+1

  = 4q2+ 4q+2q+2

  = 4q2+ 6q+2

It is divisible by 2

So, in both the case of the consecutive integers, it is divisible by 2.


HOPE IT HELPS