Consider the sequences $($an$)$and $($bn$)$in R given by an $=(1+1/$n$)^$n $,$bn $=$sigma from j$=0$to n of 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$).$