how to solve $\lim\limits_{x \to \infty} (\log x!/x \log x)$

Question

It will be appreciated if you help me to solve this limit : I'm wondering if you desribe steps of solving

$$\lim\limits_{x \to \infty} \frac{\log x!}{x \log x}$$

edit: i'm computer engineering student and i need to solve this limit that i've faced with it in "Data mining" course and "decision trees"

edit: (1 - log(x))/(log(1/x)) + (1/2 - (log(2 pi))/(2 log(1/x)))/x + O((1/x)^(3/2))

(Puiseux series)

@Dr.SonnhardGraubner The answer is independent of the base of the logarithm. — Crostul, Dec 13 '16 at 18:15
Anyway, at this Wikipedia article you can see the steps to show that the limit is $1$. — Crostul, Dec 13 '16 at 18:20
Related: http://math.stackexchange.com/questions/28476/finding-the-limit-of-frac-n-sqrtnn — Henry, Dec 13 '16 at 18:26

score 0 · Accepted Answer · answered Dec 13 '16 at 18:20

0

Hint:

Stirling's formula and equivalents. You should find $1$.

answered Dec 13 '16 at 18:20

Bernard

1 Answers1