calculating limit of a sequence

i need to calculate the limit of this sequence:

i tried to use the sandwich rule to squeeze it between to sequences, but got stuck.

this is what i did so far:

but i couldn't find anything smaller then the given sequence that can be easily calculated.

for example, i know that:

and i know that , but is it enough to say that if then also ?

thanks in advanced!!!

BTW, if there's any other way to get to the answer ( ) i'd love to hear.

Re: calculating limit of a sequence

because as . In fact, without using , the function where a > 1 monotonically decreases as x increases. Therefore, . On the other hand, for n > 1. Therefore, the fact that indeed implies that .

You could also try using Stirling's approximation.

Re: calculating limit of a sequence