How to study the convergence of this series?

Question

Is convergent series?

$$\sum_{n=1}^∞{{1}\over{n^2+2\sqrt{n}-21}}.$$

Answer 1

HINT: How does $\dfrac1{n^2+2\sqrt{n}-21}$ compare with $\dfrac1{n^2}$ when $n\ge 121$, say?

The key idea here is that the $n^2$ term is the dominant term in the denominator, so for large $n$ the denominator ought to behave much like $n^2$.