Question

The maths question for algebra is

(d) 2n + 1 is an odd number. Show that the product of 2 consecutive odd numbers is always an odd number

Can anyone please help need it fast

Answer 1

Explanation:

Let (2n +1) be the larger odd number by definition, where n can be any real integer. Then (2n - 1) is the smaller consecutive odd number.

The product of the 2 odd numbers is (2n + 1)(2n - 1) = 4n^2 - 1 = 2(2n^2) - 1. Since n^2 must be an integer, 2(2n^2) - 1 is odd. (Shown)