How to solve this sum limit? $\lim_{n \to \infty } \left( \frac{1}{\sqrt{n^2+1}}+\cdots+\frac{1}{\sqrt{n^2+n}} \right)$ How do I solve this limit?
$$\lim_{n \to \infty } \left( \frac{1}{\sqrt{n^2+1}}+\cdots+\frac{1}{\sqrt{n^2+n}} \right)$$
Thanks for the help!

Extract n from the radical. So, you have to sum n terms which are close to 1 and you divide the sum by n. Are you able to continue with this ?
