Series, computing the limit $limlimits_{ntoinfty}frac{1+2+cdots+n}{n^3}$

How to compute the following limit? The series is given by

$$\lim_{n\rightarrow\infty}\frac{1}{n^3}(1+2+\cdots+n)$$

Thanks for your help...

Answer

Just for fun:

$$\lim_{n\rightarrow\infty}\frac{1}{n}\left(\frac{1}{n}\frac{1}{n}+\frac{2}{n}\frac{1}{n}+\ldots+\frac{n}{n}\frac{1}{n}\right)=\lim_{n\rightarrow\infty}\frac{1}{n}\times\int_{0}^{1}\text{d}x=0$$