Question

Prove that (2n+1)^2 - (2n+1)^2 is a multiple of 8 for all positive integer values of n

Answer 1

(2n + 1)[(2n + 1) � 1]

(2n + 1)(2n + 1 � 1)

(2n + 1)(2n), or 2n(2n + 1)

2n is an EVEN NUMBER, and adding 1 to an even number creates an ODD number

Therefore, 2n(2n+1)=EVEN NUMBER ODD NUMBER=EVEN NUMBER

Explanation: