Question

Prove that the difference of the squares of 2 consecutive numbers is always the sum of the 2 numbers

Answer 1

see explanation

Explanation:

let the 2 consecutive numbers be n and n + 1

sum = n + n + 1 = 2n + 1

and

(n + 1)² - n² ← difference of the squares

= n² + 2n + 1 - n²

= 2n + 1 = sum of 2 numbers