Show convergence and calculate the limit: $\lim \limits_{n \to \infty}\sum \limits_{k=n}^{2n}\frac{k}{k^2+n^2}$ I guess it has something to do with Riemann sums but this is new for me.
$\displaystyle\lim \limits_{n \to \infty}\sum \limits_{k=n}^{2n}\frac{k}{k^2+n^2}$
How do I start?

Like this:
$$
\sum_{k=n}^{2n}\frac{k}{k^2+n^2}=\frac1n\sum_{i=0}^{n}\frac{1+\frac{i}n}{\left(1+\frac{i}n\right)^2+1}.
$$
