$[12]8.$ Determine whether the series is divergent or convergent, and if convergent, then whether absolutely or conditionally convergent:

$($a$){\displaystyle \underset{n=1}{\overset{}{}}}\frac{n^{\frac{2}{3}}}{1+2n}$

$($b$){\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n+1}sin(\frac{1}{n})$

$($c$){\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{(n+1)}\frac{2^{n+1}}{n!}$