21
Infinite product follow-up (links.hackliberty.org)

This is related to the the May 16 post, but takes only the prime indexed terms. Does it still diverge?

HintTransform the product into a sum


HintThe harmonic series 1 + 1/2 + 1/3 + ... 1/n +... diverges


you are viewing a single comment's thread
view the rest of the comments
[-] EyeBeam@links.hackliberty.org 4 points 5 months ago* (last edited 5 months ago)

Solution


What I like about this solution is that it doubles as a proof that there are infinitely many prime numbers. It's not circular either -- it uses the number theoretic fact that every integer has a prime factorization, but nothing deeper. If only finitely many primes were required for that, ... well then of course every finite product converges.

this post was submitted on 31 May 2024
21 points (100.0% liked)

Daily Maths Challenges

189 readers
17 users here now

Share your cool maths problems.



Complete a challenge:


Post a challenge:


Feel free to contribute to a series by DMing the OP, or start your own challenge series.

founded 6 months ago
MODERATORS