Friday, May 25, 2018

calculus - How to prove that limlimitsntoinftyfracn!n2 diverges to infinity?




lim



I can understand that this will go to infinity because the numerator grows faster.



I am trying to apply L'Hôpital's rule to this; however, have not been able to figure out how to take the derivative of \left(n-1\right)!



So how does one take the derivative of a factorial?


Answer



you could introduce the gamma function!




Just a joke, as n!>n^3 for n>100 you know that
\frac{n!}{n^2} > \frac{n^3}{n^2}=n


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