This proof demonstrates Stirling's formula by applying limits and the binomial theorem without calculus, highlighting the simplicity of foundational math concepts.
Stirling's formula has been proven in dozens of different ways. Here we provide a proof that uses no derivatives, integrals, infinite series, logarithms, or any special functions. Rather, we use only basic properties of limits, the Binomial Theorem, and inductive arguments.
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Chamberland et al. (2025) studied this question.
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