fossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 8 months agoScience memesmander.xyzimagemessage-square19fedilinkarrow-up1236arrow-down111
arrow-up1225arrow-down1imageScience memesmander.xyzfossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 8 months agomessage-square19fedilink
minus-squareKogasa@programming.devlinkfedilinkEnglisharrow-up0·8 months agoThe 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”.
minus-squareeestileib@sh.itjust.workslinkfedilinkEnglisharrow-up1·8 months agoEh, that’s just 1/2 of the harmonic sum, which diverges.
minus-squareKogasa@programming.devlinkfedilinkEnglisharrow-up1·8 months agoYes, but it proves that termwise comparison with the harmonic series isn’t sufficient to tell if a series diverges.
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”.
Eh, that’s just 1/2 of the harmonic sum, which diverges.
Yes, but it proves that termwise comparison with the harmonic series isn’t sufficient to tell if a series diverges.