Tagged Questions
1
vote
1answer
189 views
Convergence of infinite product
This could be something which is already somewhere in the website, but I am unable to locate any.
Prove $$\prod_{n=1}^{\infty} (1-z^n)$$ converges absolutely and uniformly on each compact subset of ...
7
votes
1answer
123 views
Zeros in the complex plane and convergence
I'm doing some number theory which requires some work in $\mathbb{C}$, but unfortunately my complex analysis is a little rusty.
A text I am reading states the following:
...and given that ...
3
votes
2answers
203 views
Given $\sum |a_n|^2$ converges and $a_n \neq -1$, show that $\prod (1+a_n)$ converges to a non-zero limit implies $\sum a_n$ converges.
I have been working on this problem for a while and cannot seem to make any progress without coming up with something wrong or hitting a dead end.
Here is what I have so far:
$ \prod (1+a_n) < ...
