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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.


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

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    See http://math.stackexchange.com/questions/33970/finding-the-limit-of-fracqnpn-where-q-p-are-polynomials2011-11-25
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    Terminology: if you are asking about $\lim_{n\to\infty}a_n$, that's a sequence. If you are asking about $\sum_{n=1}^{\infty}a_n$, that's a series. A geometric *series* converges if the common ratio is less than $1$ (not $0$) in absolute value. The sequence in this question is not geometric, and I'd recommend that you put some time into learning how to recognize a geometric progression when you see one, because that is a very useful skill to have.2011-11-25

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