\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that \(\sum_{k=1}^n \frac{1}{k} - \ln n\) converges to a finite limit as \(n \to +\infty\). Hint: compare the harmonic sum to \(\int_1^n dx/x = \ln n\) via Riemann sums or by a direct telescoping estimate.
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