Almost Stirling's Approximation – math.stackexchange.com

I need to prove the following bound $$n! \le e \sqrt n \left( \frac n e \right)^n$$ I can bound $\ln 1 + \ln 2 + \dots + \ln n$ as a Riemann sum with the function $\ln(n+1)$ and the trapezoidal rule: ...

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