Decide whether the series

${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n-1}\frac{3n-1}{6n-2}$

converges or diverges.

part $2$ of $3$

Decide whether the series

${\displaystyle \underset{n=1}{\overset{}{}}}(-1{)}^{n-1}\frac{\sqrt[\phantom{2}]{6n}}{1+\sqrt[\phantom{2}]{n}}$

converges or diverges.

part $3$ of $3$

Decide whether the series

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

converges or diverges.