I am trying to confirm that the series $ $ \sum_{n=1}^{\infty}\frac{\cos^2(n)}{\sqrt{n}}$ $ diverges.

However, when I try to use SumConvergence or Sum I get an unevaluated expression. Why so?

I tried

 SumConvergence[Cos[n]^2/Sqrt[n], n]  SumConvergence[(1 + Cos[2*n])/(2*Sqrt[n]), n]   Sum[ Cos[n]^2/Sqrt[n], {n, 1, Infinity}]  Sum[(1 + Cos[n])/(2 Sqrt[n]), {n, 1, Infinity}] 

However, it does not have any problems with just: $ $ \sum_{n=1}^{\infty}\frac{\cos(n)}{\sqrt{n}}$ $ which correctly states that it converges.

Also, is there a way to make Mathematica display the test that was successful? And if the Ratio Test is used, is there a way to display the sequence that was chosen to compare it to?

I should add that I am using Mathematica 11.2.0 on Windows 10 x64