Consider for all
We have: for
So we know (and thus ) is decreasing after where
So we have our two bounds.
is an= ne^-n increasing or decreasing? i think the sequence decreases for n greater than 1 and increases for n less than 1 but i only pay attention the the sequence as n goes to infitny right? also is the sequence bounded? if so how can i tell? and generally, how do i know if the sequence is bounded above?