Stirling's Approximation - Close Encounters

Stirling's Approximation is a good estimate for the factorial function. Let's explore a derivation for it. This is part of a series on combinatorics: https://www.youtube.com/playlist?list=PLH5zdqQODdBjbFarfKUmK1uG6L-DIVcR_ A full proof of Stirling's formula can be found here: https://faculty.washington.edu/moishe/hanoiex/counting/Stirling.pdf Proofs of Wallis' formula from 3 Blue 1 Brown: https://www.youtube.com/watch?v=8GPy_UMV-08 and Mathologer: https://www.youtube.com/watch?v=WL_Yzbo1ha4 Sections 0:00 Introduction 2:12 Lower and Upper Bounds 4:00 Estimating the Logarithm 7:54 Wallis' Formula 13:02 Recap