## Proof of the Sum of Square Numbers

In the first part of this series, we have counted  the number of squares on a chessboard, and we have discovered that it is equal to the sum of the squares of the first 8 positive integers. The numbers $1^2$, $2^2$, $3^2$ and so on are called  square numbers.

This method can be generalized to compute for the number of squares on larger square boards. If the measure of a board is $n \times n$, then the number of squares on it is » Read more