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Homework Statement
I try to order given functions and I am stuck with evaluating the following:
[itex]f(n)= (n+1)![/itex] and [itex]g(n)=n^{logn}[/itex]
Homework Equations
[itex]\lim_{n\to\infty}\frac{f(n)}{g(n)} = 0 [/itex]
then g(n) is faster growing.
[itex]\lim_{n\to\infty}\frac{f(n)}{g(n)} = \infty[/itex]
then f(n) is faster growing.
The Attempt at a Solution
I would guess that [itex]n^{logn}[/itex] is the faster growing function because it is exponential.
Thus, I write
[itex]\lim_{n\to\infty}\frac{(n+1)!}{n^{logn}}[/itex] and would expect the result to be zero.
My problem is that I do not know hot to take the limit of a factorial function and I also have a problem with the n^logn.
Can someone help me with this? Maybe I can write the functions in a different way?
Thanks for any help.