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## Homework Statement

I have a function [tex]a_{n}=\frac{2+3n}{2n+1}[/tex], and I have to find out whether it converges or diverges. I did the ratio test [tex]lim_{n\rightarrow\infty}\left|\frac{a_{n+1}}{a_n}\right|[/tex]. And according to the divergence test, it should diverge. Then it asks if the series, (summation of [tex]a_n[/tex]) converges or diverges.

Now my question is, if a sequence diverges, does the series converge as well?