Suppose the series converges, whether or not the series converge?
I think it does not necessarily converge, but I could not find a counterexample. Would you help me? Thank you.
Yes, so a counterexample would have to have to converge conditionally.
I think you might be able to prove that it converges, though. If the first series converges, then . Can you use this to show that the second series converges?