Using the sum of squares formula to solve more complex sums. I'm studying integration and trying to figure out how to use the sum of squares formula to solve more complicated sums. 
For example: knowing that $$\sum_{i=1}^n i^2 = \frac{n (n+1) (2 n+1)}{6}$$
how can we simplify
$$\sum_{i=1}^n (i/n)^2$$

The key  here is what anon wrote in his comment. It's helpful to expand out the terms of the sum: 
$$ \begin{eqnarray}
\sum_{i=1}^n (i/n)^2 & = & \sum_{i=1}^n \frac{i^2}{n^2}  \\
&=& \frac{1^2}{n^2} +  \frac{2^2}{n^2} + \dots + \frac{n^2}{n^2} \\
&=& \Big( \frac{{1^2} + {2^2} + \dots + {n^2}} {n^2} \Big) \\
& = & \frac{1}{n^2} \sum_{i=1}^n i^2 \\
& = & \frac{1}{n^2}  \frac{n (n+1) (2 n+1)}{6}
\end{eqnarray} $$ 
