$(10$ pts$)$ Use the Alternative Series Test to determine if the series converges.

${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^n\frac{1}{n^{2}100},{\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n}2(-1\mathrm{.}3{)}^n$

$(10$ pts$)$ Determine whether the series converges absolutely$,$ converges conditionally, or diverges.

${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n1}\frac{1}{\sqrt[\phantom{2}]{n}}$