Timeline for How to show this series converges $\sum\limits_{n=1}^\infty n^{-1/2}\sin(n)\sin(n^2)$ [closed]
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Nov 16, 2020 at 22:12 | comment | added | ursuv2 | Thank you everyone for help. I'm training for some exams and I found it. I lost like 3 hours trying to solve it. Now I got it, thank you | |
| Nov 16, 2020 at 16:31 | vote | accept | ursuv2 | ||
| Nov 16, 2020 at 13:26 | history | closed |
David Roberts♦ Desiderius Severus abx Emil Jeřábek Todd Trimble |
Not suitable for this site | |
| S Nov 16, 2020 at 9:03 | history | suggested | gmvh |
Added top-level tag
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| Nov 16, 2020 at 8:35 | review | Suggested edits | |||
| S Nov 16, 2020 at 9:03 | |||||
| Nov 16, 2020 at 8:02 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals from title
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| Nov 16, 2020 at 7:52 | comment | added | Pietro Majer | Well, indeed the sum telescopizes nicely, but the joy is immediately killed by the suspicion of homeworkness | |
| Nov 16, 2020 at 7:51 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
more descriptive title
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| Nov 16, 2020 at 7:48 | answer | added | Pietro Majer | timeline score: 10 | |
| Nov 16, 2020 at 7:33 | comment | added | Dror Speiser | Sounds like one of those "it's either trivial, or depends on the irrationality measure of pi being 2" questions :D | |
| Nov 16, 2020 at 4:15 | comment | added | user44191 | I'm pretty sure using basic trig and quadratic identities allows us to reduce @ToddTrimble 's method to whether $\sum_{n = 1}^M \sin((n + a)^2)$ and $\sum_{n = 1}^M \cos((n + a)^2)$ are bounded. That said, I suspect that while the question may not be immediately obvious, it seems unlikely to be asked with research-level understanding. | |
| Nov 16, 2020 at 1:34 | comment | added | Todd Trimble | Convergence would follow if sums of the form $\sum_{n=1}^M \sin(n)\sin(n^2)$ had an upper bound independent of $M$. This is certainly known for sums $\sum_{n=1}^M \sin(n)$. I'm sure it's also true for these sums, but I don't have an immediate proof. | |
| Nov 16, 2020 at 1:05 | review | Close votes | |||
| Nov 16, 2020 at 13:31 | |||||
| Nov 16, 2020 at 1:02 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
deleted 2 characters in body
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| Nov 16, 2020 at 0:49 | history | edited | ursuv2 | CC BY-SA 4.0 |
added 1 character in body
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| Nov 16, 2020 at 0:41 | history | edited | Konstantinos Kanakoglou | CC BY-SA 4.0 |
added 4 characters in body
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| Nov 16, 2020 at 0:31 | review | First posts | |||
| Nov 16, 2020 at 2:16 | |||||
| Nov 16, 2020 at 0:29 | history | asked | ursuv2 | CC BY-SA 4.0 |