# How do you test the alternating series Sigma (-1)^nsqrtn from n is [1,oo) for convergence?

As ${\lim}_{n \to \infty} \sqrt{n} = + \infty$ the series does not satisfy Cauchy's necessary condition and thus cannot be convergent.
Besides let ${a}_{n} = {\left(- 1\right)}^{n} \sqrt{n}$.
Clearly ${a}_{2 k} > 0$ and ${a}_{2 k + 1} < 0$ so the series oscillates indefinitely.