## University Calculus: Early Transcendentals (3rd Edition)

When $x$ approaches $0$, $\ln x$ always tends to $-\infty$ and $\dfrac{1}{n} \to 0$ as $n \to \infty$ Therefore, $\lim\limits_{n \to \infty} \ln \dfrac{1}{n}=-\infty\ne 0$ Hence, the series is divergent.