32)\cdot\;\cdots\,$?

Asked Jan 23 '22 at 16:19

Active Jan 23 '22 at 16:25

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This problem has been bothering me for a while. I know that $$(1/2)\cdot(3/4)\cdot(7/8)\cdot(15/16)\cdot(31/32)\cdot\;\cdots$$ is convergent to something other than zero (around $0.2887$), but I do not know what the exact value of it is.

I have a basic understanding of math up to calc 1 (integrals are not very solid) but is there a way to solve this problem exactly? or will I have to stick with an approximation?

edited Jan 23 '22 at 16:25

311411

3,537
9
19
36

asked Jan 23 '22 at 16:19

Brandon Nadel

2

Does this answer your question? Evaluate $\prod_{n=1}^\infty \frac{2^n-1}{2^n}$ – 311411 Jan 23 '22 at 16:23
1

Possible duplicate of Finding the value of the infinite product $\prod\limits_{n=1}^{\infty} \biggl(1-\frac{1}{2^{n}}\biggr)$ – Dietrich Burde Jan 23 '22 at 16:27

Infinite product of $(1/2)\cdot(3/4)\cdot(7/8)\cdot(15/16)\cdot(31/32)\cdot\;\cdots\,$?

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