Linked Questions

5
votes
5answers
3k views

The limit of infinite product $\prod_{k=1}^{\infty}(1-\frac{1}{2^k})$ is not 0?

Is there any elementary proof that the limit of infinite product $\prod_{k=1}^{\infty}(1-\frac{1}{2^k})$ is not 0?
5
votes
3answers
1k views

Convergence of an infinite product $\prod_{k=1}^{\infty }(1-\frac1{2^k})$? [duplicate]

Problem: I want to prove that the infinite product $\prod_{k=1}^{\infty }(1-\frac{1}{2^{k}})$ does not converge to zero. It doesn't matter to find the value to which this product converges, but I am ...
0
votes
0answers
32 views

Find the infinite product series [duplicate]

$ \lim_{n\to\infty} (1-\frac{1}{2})(1-\frac{1}{4}) \cdots (1-\frac{1}{2^n})=\prod_{n=1}^{\infty} (1-\frac{1}{2^n}) $ I've tried this techniques: 1) Using squeeze theorem, but i had not find right ...
7
votes
2answers
369 views

What is the value of $\prod_{i=1}^\infty 1-\frac{1}{2^i}$?

Also, what about in general, for some value p, which has the value 2 in the given formula? MOTIVATION: I was wondering the ...