I have faced a limit problem of $\lim\limits_{n\rightarrow\infty}\ln n!$. Now according to Stirling's approximation, we know for very large n, $\ln n!=n\ln n-n$. Now which one of the following two are correct? $$\lim_{n\rightarrow\infty}\ln n!=\lim_{n\rightarrow\infty}(n\ln n-n)$$ or $$\lim_{n\rightarrow\infty}\ln n!=(n\ln n-n)$$?
2026-05-06 10:27:38.1778063258
Stirling approximation of logarithms
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