Answer to Question #12452 in Algebra for reon

Question

prove that the difference of the squares of two consecutive natural numbers is equal to their sum

Answer 1

Let the first number be n, and the next one n+1:
(n+1)^2 - n^2 = n^2 + 2n + 1 - n^2 = 2n + 1 = n + (n+1).