5 points
Should be anything less than a harmonic decrease (that is, the nth centaur is 1/n the size of the original).
The harmonic series is the slowest-diverging series.
1 point
The assumption is that the size decreases geometrically, which is reasonable for this kind of self similarity. You can’t just say “less than harmonic” though, I mean 1/(2n) is “slower”.
2 points
2 points
Yes, but it proves that termwise comparison with the harmonic series isn’t sufficient to tell if a series diverges.
