Mathmatics

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.

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  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

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