Trying to show that this is conditionally convergent. However, i know it is convergent, but i'm struggling to show that the absolute value of this series diverges.

I am trying to use the Limit Comparison Test with 1/(n^1/2) or 1/n.

The limits either go to 0 or infinity which is of no help.

From my textbook are the conditions for the test:

– If L > 0, then an converges if and only if bn converges.

– If L = ∞ and an converges, then bn converges.

– If L = 0 and bn converges, then an converge