Question

Prove that the difference of the squares of two consecutive natural is equal to their sum.

Answer 1

Let n be a natural number.

Its consecutive natural number = n + 1

Sum of these consecutive natural numbers = n + (n +1) = 2n +1

Difference of the squares of two consecutive natural numbers

= (n + 1)² − n²

= (n + 1 − n) (n + 1 + n) {x² − y² = (x − y) (x + y)}

= 2n + 1

Thus, the difference of the squares of two consecutive natural numbers is equal to their sum.