Tuesday, 8 September 2015

limits - Result of limntoinftyfracx100nn!



The task is to lim. n is an integer. I've tried to use Stolz theorem, but that doesn't seem to give any result.




Thank you for your help.


Answer



By ratio test



\frac{{x}^{100(n+1)}}{(n+1)!}\frac{n!}{{x}^{100n}}=\frac{x^{100}}{n+1}\to 0



then



\lim_{n\to\infty} \frac{{x}^{100n}}{n!}=0


No comments:

Post a Comment

real analysis - How to find lim_{hrightarrow 0}frac{sin(ha)}{h}

How to find \lim_{h\rightarrow 0}\frac{\sin(ha)}{h} without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...