$\lim_{n \to\infty}{\left(\left(\frac{n}{n^2+1^2}\right) + \left(\frac{n}{n^2+2^2} \right)+ \dots +\left(\frac{n}{n^2+n^2} \right)\right)}$
Evaluating the limit $\lim_{n\to\infty} \left[ \frac{n}{n^2+1}+ \frac{n}{n^2+2^2} + \ldots + \frac{n}{n^2+n^2} \right]$