Stirling’s formula!

Abstract
Stirling’s approximation to n! and other estimates, some cruder, some more refined, are developed along surprisingly elementary lines. The aim is to shed some light on why these approximations work so well, for students using them to study entropy and irreversibility in such simple statistical models as might be examined in a general education physics course. At the heart of the argument is an elementary and useful representation of all the corrections to Stirling’s approximation, with which even many experts seem to be unacquainted.

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