$$\sum_{k=1}^\infty k*\ln(1-\frac{1}{k})$$ Can you apply the Raabe test for this series?I have looked at the other tests for convergence or divergence but they didn't look the same like the Raabe.
2026-03-29 20:20:45.1774815645
Determine the nature of this logarithmic series
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We have that since as $x \to 0 \implies \log(1+x) \sim x$
$$k\cdot\ln(1-\frac{1}{k}) \sim k\cdot \left(-\frac1k\right)=-1 $$
therefore the series diverges.