Evaluate the following limit: $\lim_{n\to\infty}\left(\sum_{r=1}^{n}{\frac{r}{n^{2}+n+r}}\right)$ 
Evaluate the following limit:
$$\lim_{n\to\infty}\left(\sum_{r=1}^{n}{\frac{r}{n^{2}+n+r}}\right)$$

The answer given is $\frac{1}{2}$.

Squeeze it:
$$
\frac{r}{n^2+n+n}\leq\frac{r}{n^2+n+r}\leq\frac{r}{n^2+n}
$$
