Nicomachus's Theorem/Proof 2

Proof
From the definition:
 * $\paren {n^2 - n + 1} + \paren {n^2 - n + 3} + \ldots + \paren {n^2 + n - 1}$

can be written:
 * $\paren {n^2 - n + 1} + \paren {n^2 - n + 3} + \ldots + \paren {n^2 - n + 2 n - 1}$

Writing this in sum notation: