Hi Matthew, I just read your email about the behavior of the factorial function and harmonic series for large values of nn. If you denote by γ0.5772156649\gamma \approx 0.5772156649 the Euler's number, by e2.7182818284e \approx 2.7182818284 the Euler's constant then you have the well-known Stirling's approximation:n!=2πn(ne) n(1+O(1n))n! = \sqrt{2 \pi n} {\left( \frac{n}{e} \right)}^n \left( 1 + O \left( \frac{1}{n} \right) \right)where of course I use the classical constant π3.1415926535\pi \approx 3.1415926535. We also have the following asymptotic expansion: k=1 n1k=ln(n)+γ+O(1n)\sum_{k=1}^n \frac{1}{k} = \ln(n) + \gamma + O \left( \frac{1}{n} \right)I hope that this answers your question.
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