Q: Is $\sum\_2^\infty{(-1)^n}{a\_n}$ convergent?
$$a\_n={1\over \sqrt n+(-1)^n} \space \forall n\in\mathbb{N\_{\ge2}}$$

The answer says it diverges.The only thing I could deduce is that the series is not absolutely convergent by comparison test.I tried to find a smaller diverging series but failed miserably.I guess only thing that can be done is to show the series doesn't meet
the Cauchy criterion but the difference of two partial sums looks horribly refractory to me.