True$/$False $(3$pts ea$)$

$8$ If $\underset{n}{lim}{a}_n=0$ then ${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ converges.

$9.$ If ${\displaystyle \underset{?}{\overset{?}{}}}{a}_n$ converges then $\underset{n}{lim}{a}_n=0.$

$10.$ The Ratio Test works well for

${\displaystyle \underset{n=0}{\overset{}{}}}\frac{1}{n^2}$

$$ The series

is Absolutely Convergent.

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

$$ If ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n{\displaystyle \underset{n=1}{\overset{}{}}}{b}_n{\displaystyle \underset{n=1}{\overset{}{}}}{a}_n{\displaystyle \underset{n=1}{\overset{}{}}}{b}_{n}0$ and ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ diverges then ${\displaystyle \underset{n=1}{\overset{}{}}}{b}_n$ also diverges$\mathrm{.}0$ and ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ converges then ${\displaystyle \underset{n=1}{\overset{}{}}}{b}_n$ also converges.

$If0$ and ${\displaystyle \underset{n=1}{\overset{}{}}}{a}_n$ diverges then ${\displaystyle \underset{n=1}{\overset{}{}}}{b}_n$ also diverges.