Question Number 101003 by bachamohamed last updated on 29/Jun/20
$$\:\boldsymbol{{What}}\:\boldsymbol{{is}}\:\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{x}}\:\boldsymbol{{for}}\:\boldsymbol{{wich}}\:\boldsymbol{{the}}\:\boldsymbol{{serie}}\:\boldsymbol{{is}}\:\boldsymbol{{converge}}?\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\left(\mathrm{1}\right)\:\underset{\boldsymbol{{n}}\geqslant\mathrm{0}} {\sum}\boldsymbol{{x}}^{\frac{\boldsymbol{{ln}}\left(\boldsymbol{{n}}\right)}{\boldsymbol{{n}}!}} \:?\:\:\:\:\:\:\left(\mathrm{2}\right)\:\underset{\boldsymbol{{n}}\geqslant\mathrm{0}\:} {\sum}\boldsymbol{{x}}^{\frac{\boldsymbol{{ln}}\left(\boldsymbol{{n}}!\right)}{\boldsymbol{{n}}}} \:? \\ $$$$ \\ $$