Mathematics

Prove that the sum of two consecutive odd numbers is divisible by 4.

3 Likes

Let two consecutive odd numbers be (2n + 1) and (2n + 3) for some integer n.

Sum = (2n + 1) + (2n + 3)

= 4n + 4

= 4(n + 1).

On dividing the sum by 4, we get :

$\Rightarrow \dfrac{4(n + 1)}{4}$ = n + 1.

Hence, proved that sum of two consecutive odd numbers is divisible by 4.

Answered By

1 Like