Is it sufficient to prove that ? What do you think? The successive absolute differences are non-increasing.
Or will we also have to prove that it's bounded? (Which seems pretty obvious.)
I wasn't quite seeing it. I was hoping I could get one of you'all to talk me into it.
It was rather weak to rely on "non-increasing". Since the sequence would quikly leave the Domain if it had to stick with equality, it would be stronger to state "decreasing", but that remains only as convincing as the Harmonic example.
Well, Mark84, what are your thoughts? What is it about that slope that ensures convergence?