$($a$)$ Check all of the following that are true for the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{ln(4n)+8n}{n^2}$

A$.$ This series converges

B$.$ This series diverges

C$.$ The integral test can be used to determine convergence of this series.

D$.$ The comparison test can be used to determine convergence of this series.

E$.$ The limit comparison test can be used to determine convergence of this series.

F$.$ The ratio test can be used to determine convergence of this series.

G$.$ The alternating series test can be used to determine convergence of this series.

$($b$)$ Check all of the following that are true for the series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{8^n}{4^n-1}$

A$.$ This series converges

B$.$ This series diverges

C$.$ The integral test can be used to determine convergence of this series.

D$.$ The comparison test can be used to determine convergence of this series.

E$.$ The limit comparison test can be used to determine convergence of this series.

F$.$ The ratio test can be used to determine convergence of this series.

G$.$ The alternating series test can be used to determine convergence of this series.