Let $$a_n = \frac{3n}{6n+13}.$$ For the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter 'infinity' if it diverges to $\infty$, '-infinity' if it diverges to $- \infty$ or 'DNE' otherwise.

(a) The series $\displaystyle \sum_{n=1}^\infty \frac{3n}{6n+13}$.  

(b) The sequence $\displaystyle \biggl \lbrace \frac{3n}{6n+13} \biggr \rbrace$.