For each of the following series, indicate whether the integral test can be used to determine its convergence or not, and if not, why.

A$.{\displaystyle \underset{n=2}{\overset{}{}}}\frac{n^8}{n^{7}ln(n)}$

Can the integral test be used to test convergence?

No$,$ because the terms in the series do not decrease in magnitude

No$,$ because the terms in the series aren't all positive $($for sufficiently large $n)$

No$,$ because the series is not a geometric series

No$,$ because the terms in the series are not recursively defined

No$,$ because the terms in the series are not defined for all $n$

YYes

B$.{\displaystyle \underset{n=1}{\overset{}{}}}\frac{cos(n)}{n^8}$

Can the integral test be used to test convergence?

No$,$ because the terms in the series do not decrease in magnitude

No$,$ because the terms in the series aren't all positive $($for sufficiently large $n)$

No$,$ because the series is not a geometric series

No$,$ because the terms in the series are not recursively defined

No$,$ because the terms in the series are not defined for all $n$

Yes