Does the sequence decrease and converge to zero?
That is the alternating series test.
Now does the series converge?
If not then the convergence is not absolute.
Thanks for the response!
Ok, so I got a response back from my professor. It is true that the series diverges. But with the it converges conditionally. I was confused, because I just thought that if a series is divergent, it's divergent. Period. I think I just assumed that for a series to be conditionally convergent, it began as convergent and due to making a change to it i.e. made it be conditionally convergent. Anyway, looks like I solved it correctly on my test, but didn't look at the series long enough to realize that it was actually divergent.