How to evaluate $\lim\limits_{n\to\infty}\frac{1}{n}((x+\frac{a}{n})^2+(x+\frac{2a}{n})^2+...+(x+\frac{(n-1)a}{n})^2)$ I don't know how to transform the expression $\frac{1}{n}((x+\frac{a}{n})^2+(x+\frac{2a}{n})^2+...+(x+\frac{(n-1)a}{n})^2)$
The solution, after transformation is 
$\frac{n-1}{n}x^2+2\frac{1+...+(n-1)}{n^2}ax+\frac{1^2+...+(n-1)^2}{n^3}a^2$
Thanks for replies.

Hint:
$$1 + \cdots + (n - 1) = \frac{n(n-1)}{2} = \frac{n^2}{2} - \frac{n}{2}$$
and
$$
1^2 + 2^2 + \cdots + (n - 1)^2 = \frac{(n-1)n(2n-1)}{6} = \frac{n^3}{3} - \frac{n^2}{2} + \frac{n}{6}$$
