Timeline for "Find $\lim_{n \to \infty}\frac{x_n}{\sqrt{n}}$ where $x_{n+1}=x_n+\frac{n}{x_1+x_2+\cdots+x_n}$" -where does this problem come from?
Current License: CC BY-SA 4.0
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| Jul 10, 2022 at 21:15 | vote | accept | Paresseux Nguyen | ||
| Jul 10, 2022 at 21:15 | comment | added | Paresseux Nguyen | @CarloBeenakker: Thank you for your answer. | |
| Jul 10, 2022 at 20:47 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 10, 2022 at 17:56 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 10, 2022 at 17:50 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 10, 2022 at 17:39 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 10, 2022 at 17:33 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 10, 2022 at 14:11 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 10, 2022 at 14:02 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 10, 2022 at 13:52 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 10, 2022 at 13:47 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 10, 2022 at 13:40 | comment | added | Carlo Beenakker | @ParesseuxNguyen --- indeed, I would not know how to prove the existence of the limit from the SC theorem; I have removed that sentence. | |
| Jul 10, 2022 at 13:39 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Jul 10, 2022 at 13:32 | comment | added | Will Jagy | Thank You! ${}{}{}{}{}$ | |
| Jul 10, 2022 at 13:26 | comment | added | Carlo Beenakker | @WillJagy --- here is a screenshot | |
| Jul 10, 2022 at 13:10 | comment | added | Will Jagy | Carlo, it is in a book by the same pair of authors that the suggestion of "open problem" comes up. Called Sharpening Mathematical Analysis Skills. Also, in a section 1.30 called "Open Problems," where this problem is a special case of the "open" problem specified there. I would be happy just to see the relevant page. | |
| Jul 10, 2022 at 7:26 | comment | added | Paresseux Nguyen | By "that theorem", did you mean Stolz-Cesàro's? Would you mind clarifying this point? Because, I think the crucial part of this problem is to prove the existence of the limit. Nonetheless, to the best of my knowledge, Stolz-Cesàro's cannot show that. | |
| Jul 10, 2022 at 7:20 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |
