Doubt from maxima and minima

\frac{n(n+1)}{2e}<\sum_{k=1}^{n}{(k!)^{\frac{1}{k}}}<\frac{31}{20}+\frac{n(n+1)}{4}. @Hari_Shankar sir , @Jagdish_Singh sir
@Mayank_2019_1 sir please see it sir thanks..

how to get upper bound.. @Ajay_2021.