Oresme's proof: grouping shows divergence
1 + 1/2 + (1/3+1/4) + (1/5+…+1/8) + …
Each group ≥ 1/2: 1/3+1/4 > 2×1/4 = 1/2 and 1/5+…+1/8 > 4×1/8 = 1/2
We can always add another group ≥ 1/2, so the total grows without bound. QED (Oresme ~1360)
H(n) grows like ln(n) plus γ
H(n) and ln(n) grow together, always differing by approximately γ ≈ 0.5772. Both diverge: to reach H(n) = 100 requires about 10^43 terms.
How absurdly slow: milestones for H(n) exceeding round numbers
~10^43 terms are needed to reach H(n)=100. More than atoms in the observable universe.
Digunakan dalam
Matematika
✓
Fisika
✓
Teknik
–
Biologi
–
Ilmu Komputer
✓
Statistika
–
Keuangan
–
Seni
–
Arsitektur
–
Musik
✓
Kriptografi
–
Astronomi
–
Kimia
–
Filsafat
–
Geografi
–
Ekologi
–
Ingin menguji pengetahuan Anda?
Pertanyaan
Apa itu teorema penyusunan ulang Riemann?
ketuk · spasi
1 / 10
Siap bermain?
Pi
Memorize pi, e, and 40+ mathematical constants using the numpad path method
Main sekarang - gratisTanpa akun. Bisa di perangkat apa saja.
Topic roundups
