Comment on Science memes
eestileib@sh.itjust.works 5 months agoShould 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.
Comment on Science memes
eestileib@sh.itjust.works 5 months agoShould 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.
kogasa@programming.dev 5 months ago
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”.
eestileib@sh.itjust.works 5 months ago
Eh, that’s just 1/2 of the harmonic sum, which diverges.
kogasa@programming.dev 5 months ago
Yes, but it proves that termwise comparison with the harmonic series isn’t sufficient to tell if a series diverges.
eestileib@sh.itjust.works 5 months ago
Very well, today I accede to your superior pedantry.
But one day I shall return!