Question Number 204900 by universe last updated on 01/Mar/24
$$\:\:\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{n}!\left({e}−\mathrm{x}_{\mathrm{n}} \right)\:=\:? \\ $$$$\:\:\mathrm{where}\:\mathrm{x}_{\mathrm{n}\:} =\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}}{\mathrm{2}!}+…+\frac{\mathrm{1}}{\mathrm{n}!} \\ $$
Commented by Frix last updated on 01/Mar/24
$${x}_{{n}} \rightarrow\mathrm{e}\:\Rightarrow\:\mathrm{Answer}\:\mathrm{is}\:\mathrm{0} \\ $$
Commented by JDamian last updated on 02/Mar/24
$${But}\:\:\:\:{n}!\:\rightarrow\:\infty\:\:\:\:\Rightarrow\:\:\:\infty\centerdot\mathrm{0} \\ $$