Consider the sequences $($an$)$ and $($bn$)$ in R given by an $=(1+1/$n$)^$n $,$ bn $=$ sigma from j$=01$ to n j$!.$ Recall that $($an$),($bn$)$ are strictly increasing, and limn$$ an $=$ limn$$ bn $=$ e$.$ Determine limn$$ n$($e $$ an$)$ as well as limn$$ n$!$n$($e $$ bn$).$