Evaluation of Integral sums Hey I am supposed to evaluate: $$\lim_{n \to \propto }\sum_{i=1}^{n}\frac{i}{n^{2}+i^{2}}$$
What I did:
$$\lim_{n \to \propto }\sum_{i=1}^{n}\frac{i}{n^{2}+i^{2}}=\lim_{n \to \propto }\frac{1}{n^{2}}\sum_{i=1}^{n}\frac{i}{1+\left ( \frac{i}{n} \right )^{2}}$$
But I do not know, what to do next, or how to eliminate i so I can transfer it to integral.
Can anyone help me?

$$\dfrac r{n^2+r^2}=\dfrac1n\cdot\dfrac{r/n}{1+(r/n)^2}$$
Now use The limit of a sum $\sum_{k=1}^n \frac{n}{n^2+k^2}$
