sequences and series - How to know if it diverges or converges and finding the convergent value

I am given the following succession/series/sequence:

$$a_n = \frac{4n^5 +4n^3+n}{5n^4-2n^5+n^2}$$

How do I find out if it converges or diverges and how to find such values.

I am quite lost on the subject.

I've read that in a Geometric succession/series/sequence it is convergent if the ratio is less than 0, but I'm not sure if its a geometric series.

Help is really appreciated, thanks in advance.

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PD: My native language is not english so I'm not sure what the appropriate term would be, is it succession, series or sequence.