What sums equal x2?

Answer 1

The sum of the first x odd numbers is equal to x2 (for integers only.)

For example, take 72: We'll take the first seven odd numbers:

1 + 3 + 5 + 7 + 9 + 11 + 13

= 4 + 12 + 20 + 13

= 16 + 33

= 49

This then, can be expressed as follows:

    x

x2 = Σ(2n - 1)

   n=1