scterg

4 ms·

1. 1.▲
   by scterg 3y ago

   Indeed. I didn't realize "diverging to zero" with a thing either. I do think this is what the author had in mind, since he writes about the sum of the logs, "whose convergence is equivalent to the convergence of the prod
2. 2.▲
   by scterg 3y ago

   See the wiki link in a previous comment: https://en.wikipedia.org/wiki/Infinite_product "The product is said to converge when the limit exists and is not zero." #1. Consider the series 1 - 1/2^(1/2)
3. 3.▲
   by scterg 3y ago

   Re: #1. Found an example using complex numbers. Still can't think of one using the reals though. EDIT: learned about "diverge to zero", where the product goes to zero but the series is still said to "diverge" (since
4. 4.▲
   by scterg 3y ago

   Not sure about #1. Is it impossible? Convergence of the sum of a_n implies a_n goes to zero, which means we can use the theorem, right? What am I missing? #2. Consider the sequence 1, -1/2, 1, -1/2, .... The sum diverges while the