Main Question or Discussion Point
The harmonic series is divergent, and in general, I know that just because one series is larger than another divergent series, doesn't mean the series is convergent. However, the harmonic series is very, very slow to diverge. Is the harmonic series the slowest diverging series? That is, is it the case that any series larger than the harmonic series must necessarily converge and is there any easy proof to show this?