Question

Prove algebraically that the difference between the square of any two consecutive integers is equal to the sum of these two integers.

First number = n
Second number = n+1

Square the second number: (?????)^2

Difference between the squares: ?????

Sum of the consecutive integers = ? + ? = ?

Thank you.

Answer 1

If the two numbers are n and n+1, then we have

(n+1)^2 - n^2
= n^2+2n+1-n^2
= 2n+1
= n + n+1