How do I show that this series is conditionally convergent?

$$\sum_{n=1}^\infty \cos(n\pi)\sin\left(\frac{\pi}{\sqrt {n}}\right)$$

I know that to show that a series is conditionally convergent, I will have to show that the series is convergent, and also show that the absolute value of the series is divergent.

I am able to show that $$\sum_{n=1}^\infty \cos(n\pi)\sin\left(\frac{\pi}{ \sqrt n}\right)$$ is convergent using the alternating series test, where the limit is equals to 0 and the expression is non-increasing. But I have no idea how to show that the absolute value of the series is divergent. Please correct me if my concept is wrong.