$($a$)(6$ points$)$ Determine whether the series converges or diverges. If it converges, compute the sum.

${\displaystyle \underset{n=1}{\overset{}{}}}{5}^{n-1}{3}^{1-2n}$

$($b$)(4$ points$)$ Determine whether the series converges or diverges, and justify this determination.

${\displaystyle \underset{m=2}{\overset{}{}}}\frac{1}{m-1}$

$($c$)(6$ points$)$ Determine whether the series converges or diverges, and justify this determination.

${\displaystyle \underset{k=1}{\overset{}{}}}\frac{1}{klnk}$