Question
How to show working for limit of n to infinity [(n^10)/n!]?
I know it should be 0 by order of hierarchy where n!>n^10 but I am not sure how to show working.
I know it should be 0 by order of hierarchy where n!>n^10 but I am not sure how to show working.
Answers
Steve
(n+1)^10/(n+1)!
--------------------------
n^10/n!
= (n+1)^10/n^10 * 1/(n+1)
(n+1)^10/n^10 -> 1
so by the ratio test the sequence converges
--------------------------
n^10/n!
= (n+1)^10/n^10 * 1/(n+1)
(n+1)^10/n^10 -> 1
so by the ratio test the sequence converges