University Calculus: Early Transcendentals (3rd Edition)

For this series $\Sigma_{n=1}^\infty \dfrac{-2}{n\sqrt n}=-2\Sigma_{n=1}^\infty \dfrac{1}{n^{3/2}}$ Thus, the given series is a p-series with $p=\dfrac{3}{2} \geq 1$ Hence, the given series converges.