Let

$a_n=\frac{6n}{2n+5}$

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 seriej$).$ If divergent, enter 'infinity' if it diverges to $,\text{'}-$infinity' if it diverges to $-$ or 'DNE' otherwise.

$($a$)$ The series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{6n}{2n+5}.$

$($b$)$ The sequence $\{\frac{6n}{2n+5}\}.$