How would I find if the series converges or diverges using the Direct Comparison Test?

Question

I do not understand the Direct Comparison test at all so I need a walk through, because I read the examples and none of it makes sense to me. Here we go, the problem reads:

Use the Direct Comparison Test to determine whether this series converges or diverges?

$$\sum_{n=1}^\infty \frac {n^2}{(n^3+1)^{1.01}}$$

I'm still uncertain on how I will break this up and etc. Please help.

Answer 1

Hint: $$\frac {n^2}{(n^3+1)^{1.01}}\sim \frac{n^2}{n^{3,03}}=\frac1{n^{1.03}}$$