Hi.

Ho can i show that $\displaystyle \lim_{n\rightarrow \infty}\frac{n\ln n}{\ln n!}=1$?

I tried to use the sandwich rule to say that:

$\displaystyle \frac{n\ln n}{\ln n!}\geq \frac{n\ln n}{\ln n^n}=\frac{n\ln n}{n\ln n}=1$

but couldn't find anything bigger to squeeze it between.

what other ways are there to evaluate the limit here?

any guidance would greatly appreciated.

thanks in advanced!