Determine whether the series given below converge conditionally, converge absolutely, or diverge.
$\qquad\displaystyle\sum\limits_{n=1}^{\infty }{\frac{{{\left( -1 \right)}^{n}}}{1+\frac{1}{n}}}$
[[☃ radio 1]]
$\qquad\displaystyle\sum\limits_{n=2}^{\infty }{\frac{{{\left( -1 \right)}^{n}}}{n\ln n}}$
[[☃ radio 2]]
$\qquad\displaystyle \sum\limits_{n=1}^{\infty }{\frac{{{\left( -1 \right)}^{n+1}}}{\sqrt{n}}}$
[[☃ radio 3]]