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