University Calculus: Early Transcendentals (3rd Edition)

We need to apply The Integral Test. Thus, $\int_{1}{n} \dfrac{5}{x+1}dx=5 \ln (n+1)-5 \ln 2$ or, $\int_{1}{\infty} \dfrac{5}{x+1}dx=\infty$ Thus, the series is divergent