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