I am working on a series and attempting to determine its conditional convergence using the alternating series test.
$$ \sum_{n=1}^{\infty} \frac{\cos\left(\frac{\pi}{4} + 2\pi n\right)}{\sqrt{n}} $$
I think it satisfies the conditions for the alternating series test: it alternates sign due to the cosine term, and the absolute values of the terms appear to be decreasing as n increases. However, the solution manual for my textbook suggests that the series is diverging. Am I correct in using the alternating series test?