Answer
Convergent
Work Step by Step
Consider the series $\Sigma_{n=1}^\infty \dfrac{-2}{n\sqrt n}$
It can be re-written as: $\Sigma_{n=1}^\infty \dfrac{-2}{n\sqrt n}=-2\Sigma_{n=1}^\infty \dfrac{1}{n^{3/2}} $
This shows that the series is a $p$-series with $p=\dfrac{3}{2} \geq 1$
Thus, the series is convergent.