Sum of Sequence of Squares/Proof by Summation of Summations

Proof

 * [[File:Sum of Sequences of Squares.jpg]]

We can observe from the above diagram that:
 * $\ds \forall n \in \N: \sum_{i \mathop = 1}^n i^2 = \sum_{i \mathop = 1}^n \paren {\sum_{j \mathop = i}^n j}$

Therefore we have: