## series Converges.

When I say a series $\sum$a$_{n}$ converges, what exactly is it that I am saying?
for example
$\sum^{∞}_{n=1}$$\frac{9n^{2}}{3n^{5}+5}$ is convergent. what did I just say?
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 Recognitions: Gold Member Science Advisor Staff Emeritus Why would you say a series converges if you don't know what it means? If you have taken a course dealing with sequences and series, then you should have seen a definition of "convergence of a sequence": the series $\sum_{n=1}^\infty a_n$ converges if and only if the sequence of partial sums $s_i= \sum_{n= 0}^i a_n$ converges. (I hope you won't say that $\sum_{n=1}^\infty \frac{9n^2}{3n^2+ 5}$ is convergent. It obviously isn't.)
 Congrats on telling me exactly what the book told . so now if you don't mind tell it to me as if I was not a person studying Mathematics .

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