TITLE: Limit Comparison Test Question
QUESTION [6 upvotes]: I'm trying to find the end behavior of
$$\sum_{n=1}^{\infty}\frac{1}{\sqrt{n^2+1}}$$
using the limit comparison test, but I'm having a hardtime finding the comparing equation. I would appreciate if someone could either give me advice to finding the comparing equations and/or the equation of the this problem.
Thanks in advance.

REPLY [5 votes]: The one that came first to my mind was:
$\sum_{n=1}^{\infty}\frac{1}{\sqrt{n^2+1}}$ $>$ $\sum_{n=1}^{\infty}\frac{1}{\sqrt{n^2+2n+1}}$ $=$
$=$ $\sum_{n=1}^{\infty}\frac{1}{{n+1}}$ $=$ $\infty$ $\hspace{99mm} \blacksquare$