This is related to the the May 16 post, but takes only the prime indexed terms. Does it still diverge?
Hint
Transform the product into a sum
Hint
The harmonic series 1 + 1/2 + 1/3 + … 1/n +… diverges
This is related to the the May 16 post, but takes only the prime indexed terms. Does it still diverge?
Transform the product into a sum
The harmonic series 1 + 1/2 + 1/3 + … 1/n +… diverges
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.