I need to judge whether the series $\sum_{n=1}^{\infty}(-1)^{n}\left(1-\cos \frac{\alpha}{n}\right)$ (α>0) is absolutely convergent.
SumConvergence[(-1)^n (1 - Cos[α/n]), n]
SumConvergence[Abs[(1 - Cos[α/n])], n, Method -> Automatic]
SumConvergence[Abs[(1 - Cos[1/n])], n, Method -> Automatic]
But the above code can not determine whether the series is absolutely convergent. How can I solve this problem?