can you use absolute convergence test to prove divergence?
to my understanding, if the absolute value of a series converges, then by absolute convergence test, the original series will also converge.
additionally, i am aware that if the original series converges and the absolute value of the series does not, the series is conditionally convergent.
however, what if you don't know the original series' behavior? would applying the absolute convergence test and seeing that it diverges tell you nothing ? and therefore would you need to use a different test?