Determinte whether a_n is convergent for...

[tex] a_n = \frac{2n}{3n+1}[/tex]

How would i go about solving this? Can i just simply take the limit and use L'Hospital's rule to see if it diverges or converges? Or is it a little more complicated than that? Im asking this because in this section we're studying geometric series, and that doesnt look like a geo series to me since n is not in the exponent. Any help would be appreciated, thanks.