We're supposed to use the alternating series to say if this diverges or converges and if we do not know what it does using the alternating series test (regardless of what another test says) then we need to state that as well.

However, the answer to the question is that it converges and since the question wants us to only use the alternating series test. Here is what confuses me: The limit DOES go to zero which is good but it does not seem to be decreasing! I tried b_n and b_(n+1) and it seems to increase instead. Am I doing something wrong?

Any input would be greatly appreciated!

Thanks in advance!