Tuesday, 8 September 2015

limits - Result of limntoinftyfracx100nn!



The task is to limnx100nn!. 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



x100(n+1)(n+1)!n!x100n=x100n+10



then



limnx100nn!=0


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