\[\underset{x+\infty}{\mathop{\lim}}\,\left( \frac{n}{{{n}^{2}}+{{1}^{2}}}+\frac{n}{{{n}^{2}}+{{n}^{2}}}+\frac{n}{{{n}^{2}}+{{3}^{2}}}+...\frac{1}{5n} \right)\] is equal to:
\[\underset{x\to \infty }{\mathop{\lim }}\,\sum\limits_{r\,=\,1}^{2n}{\frac{1}{n\left( 1+\frac{{{r}^{2}}}{{{n}^{2}}} \right)}}\] Using D.I as limit of sum, we get