Timeline for Difference between finite partial sums from two divergent series
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28 at 17:09 | vote | accept | Sanae Kochiya | ||
| Aug 28 at 9:54 | answer | added | Pietro Majer | timeline score: 3 | |
| Aug 28 at 1:11 | comment | added | Sanae Kochiya | @IosifPinelis Hopefully a condition described in terms of the given sequence $(r_n)_{n\in \mathbb{N}}$. I am not optimistic to see a condition that includes "for all..." but hopefully something weaker. In fact, it would be also helpful to see an example. | |
| Aug 28 at 1:05 | history | edited | Sanae Kochiya | CC BY-SA 4.0 |
added 65 characters in body
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| Aug 28 at 1:01 | comment | added | Sanae Kochiya | @PietroMajer I see what you mean. It will be more accurate to write: $$\left\vert\, \sum_{N\leq i \leq M}r_i - \sum_{N\leq i \leq M}s_i\,\right\vert < \dfrac{\epsilon}{2}$$ whenever $\sum_{N\leq i \leq M} r_i\in \left( \dfrac{\epsilon}{2}, \epsilon \right)$. All I want is that $\sum_{N\leq i \leq M}s_i$ can be small enough to be close to $\sum_{N\leq i \leq M}r_i$ when $\sum_{N\leq i \leq M}r_i$ is arbitrarily small. | |
| Aug 27 at 17:37 | comment | added | Pietro Majer | Do you really mean the intervals to be $(\frac\epsilon2,\epsilon)$ and $(\epsilon,2\epsilon)$ or it's just a typo? | |
| Aug 27 at 17:26 | comment | added | Iosif Pinelis | In what non-tautological terms do you want such a necessary condition to be described? | |
| Aug 27 at 17:01 | history | asked | Sanae Kochiya | CC BY-SA 4.0 |