Question Number 210200 by Erico last updated on 02/Aug/24
$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\forall\mathrm{n}\geqslant\mathrm{4}\:\:\:\:\:\:\:\mathrm{n}!\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{n}}}\right)\:\leqslant\:\underset{\:\mathrm{0}} {\int}^{\:\mathrm{n}} \mathrm{t}^{\mathrm{n}} \mathrm{e}^{−\mathrm{t}} \mathrm{dt}\:\leqslant\:\frac{\mathrm{n}!}{\mathrm{2}} \\ $$