Timeline for Is there a known condition for partial sums of a decreasing positive sequence to take all values up to the total sum?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 19, 2021 at 22:03 | vote | accept | John Bentin | ||
| May 26, 2020 at 7:02 | comment | added | John Bentin | @MiloBrandt : Your answer showed the sufficiency of the bound $a_n \leq \sum_{m > n}a_m$, but not the necessity (which wasn't needed to answer the question). | |
| May 26, 2020 at 1:56 | comment | added | Milo Brandt | I wrote an answer a while ago on Math Stack Exchange that answered exactly this: here. I think it's entirely in line with Will Brian's answer. | |
| May 26, 2020 at 1:29 | history | became hot network question | |||
| May 25, 2020 at 19:16 | answer | added | Will Brian | timeline score: 17 | |
| May 25, 2020 at 19:15 | answer | added | Iosif Pinelis | timeline score: 6 | |
| May 25, 2020 at 18:54 | comment | added | Will Brian | OK, thanks -- I'll see if my idea works, and write an answer if it does :) | |
| May 25, 2020 at 18:54 | comment | added | John Bentin | @WillBrian : Yes, your sum condition doesn't involve indices comprising arbitrary subsets of $\Bbb N$, only terminal segments of $\Bbb N$. So it's not just a rewrite of the originally stated property. | |
| May 25, 2020 at 18:39 | comment | added | Will Brian | I think it's necessary and sufficient to have $a_n \leq \sum_{m > n}a_m$ for all $n$. Is this the kind of condition you have in mind? I'm not sure what you mean by "not involving arbitrary partial sums". | |
| May 25, 2020 at 18:32 | comment | added | Will Brian | Even deleting a single term (other than the first term) from the sequence $a_n = 1/2^n$ makes it no longer have your property. | |
| May 25, 2020 at 17:25 | history | asked | John Bentin | CC BY-SA 4.0 |