As n → ∞, n! ≈ √(2πn) · (n/e)^n with relative error O(1/n). Proved via Euler-Maclaurin, complex Laplace method, or the Γ-function integral. First term in a full asymptotic expansion n! = √(2πn)(n/e)^n · (1 + 1/(12n) + 1/(288n²) − …). Key…
As n → ∞, n! ≈ √(2πn) · (n/e)^n with relative error O(1/n). Proved via Euler-Maclaurin, complex Laplace method, or the Γ-function integral. First term in a full asymptotic expansion n! = √(2πn)(n/e)^n · (1 + 1/(12n) + 1/(288n²) − …). Key…