Determine if the following alternating series converges absolutely, converges conditionally, or diverges.

 $\displaystyle {\sum_{{{n}={1}}}^{\infty}}\frac{{{\left(-{1}\right)}^{{n}}{2}^{{{2}{n}+{1}}}}}{{{\left({2}{n}+{1}\right)}!}}$ 

1.  List the series test(s) that you use.

2.  Show your reasoning and steps.

3.  State your conclusion:  converges absolutely, converges conditionally, or diverges