How do you determine the convergence or divergence of Sigma ((-1)^(n))/(sqrtn) from [1,oo)?

${\sum}_{k = 1}^{\infty} {\left(- 1\right)}^{k} / \sqrt{k}$
is an alternate series with $\left\mid {a}_{k} \right\mid < \left\mid {a}_{k - 1} \right\mid$ so it converges.
Here ${a}_{k} = \frac{1}{\sqrt{k}}$.