Timeline for Prove that if $\sum_{t=1} ^{\infty} x_t = \infty$ where $x_t \in [0,1], \forall t$, then $\prod_{t = 1}^{\infty} (1-x_{t}) = 0$ [closed]
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Dec 2, 2019 at 9:16 | comment | added | Martin Sleziak | @thanhtang Well, for math expressions searching is not easy, but if it helps, here is some advice specific to Mathematics: How to search on this site? In this case I'd guess that quick ways could be using Approach0 or checking the frequent tab of the tag (infinite-product). | |
| Dec 2, 2019 at 5:31 | comment | added | ttt | @MartinSleziak: Didn't know this question had been asked on math.stackexchange because I forgot the name "infinite product" to search for. I have found a solution but thanks anyway for the pointers. | |
| Dec 1, 2019 at 6:06 | comment | added | Martin Sleziak | Some posts on Mathematics where this is shown: Infinite product problem, Suppose $1>a_n>0$ for $n\in \mathbb{N}$. Prove that $\prod_{n=1}^\infty (1-a_n)=0$ converges if and only if $\sum_{n=1}^\infty a_n=\infty$., How to prove $\prod_{i=1}^{\infty} (1-a_n) = 0$ iff $\sum_{i=1}^{\infty} a_n = \infty$?, etc. | |
| Dec 1, 2019 at 4:12 | comment | added | ttt | @GHfromMO: Yes, I agree that math.stackexchange seems like a better fit for this question. Please consider closing it. Thanks for the notice and clarification. | |
| Dec 1, 2019 at 2:52 | history | closed |
Andreas Blass Andrés E. Caicedo GH from MO LSpice Keshav Srinivasan |
Not suitable for this site | |
| Dec 1, 2019 at 2:31 | comment | added | GH from MO | Just use that $0\leq 1-x_t<e^{-x_t}$, and multiply these inequalities. At any rate, this is not a research level question, it would be more suitable for math.stackexchange.com | |
| Dec 1, 2019 at 2:09 | comment | added | ttt | $(x_t)$ is a sequence indexed by $t \in \mathbb{N}$. | |
| Dec 1, 2019 at 2:02 | answer | added | ttt | timeline score: 0 | |
| Dec 1, 2019 at 1:45 | comment | added | Amir Sagiv | What does the notation $x_t$ stand for? Is it just an indexing scheme, or do we know something on the dependence of $x$ on $t$? | |
| Dec 1, 2019 at 1:25 | review | Close votes | |||
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| Dec 1, 2019 at 1:16 | answer | added | Igor Rivin | timeline score: 1 | |
| Dec 1, 2019 at 1:10 | review | First posts | |||
| Dec 1, 2019 at 1:45 | |||||
| Dec 1, 2019 at 1:07 | history | asked | ttt | CC BY-SA 4.0 |