Chapter 4.7, Problem 116E

Factorial growth rate The factorial function is defined for positive integers as $n!=n(n-1)(n-2)\cdots 3\cdot 2\cdot 1$. For example, 5! = 5 · 4 · 3 · 2 · 1 = 120. A valuable result that gives good approximations to n! for large values of n is Stirling’s formula, $n!\approx \sqrt{2\pi n}{n}^n{e}^{-n}$. Use this formula and a calculator to determine where the factorial function appears in the ranking of growth rates given in Theorem 4.15. (See the Guided Project Stirling’s Formula.)