Let $S(n)=\sqrt{2\pi n}\big(\frac{n}{e}\big)^n$ be the approximation of interest to $n!$.
What are good lower and upper bounds on the following two functions $$(1)\mbox{ }|S(n)-n!|?$$ $$(2)\mbox{ }\frac{S(n)}{n!}?$$
2026-03-26 06:03:09.1774504989
Additive and Multiplicative Error in $n!$ Approximation
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