Find $\lim\limits_{n\to +\infty}\big(\frac{1}{\sqrt{n^2 + 1}} + \frac{1}{\sqrt{n^2 + 2}} + \cdots + \frac{1}{\sqrt{n^2 + n}}\big)$?
Compute the limit of the sequence ${\textstyle\sum_{k=1}^n}\frac1{\sqrt{n^2+k}}$