Timeline for Limit of $\frac{1}{n}\sum_{r=1}^n\frac{n\ (\mathrm{mod}\ r)}{r}$
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Jul 25, 2017 at 22:32 | history | edited | GH from MO |
edited tags
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| Apr 17, 2012 at 19:45 | comment | added | Woett | Then I said nothing :) | |
| Apr 17, 2012 at 19:41 | comment | added | Gerhard Paseman | Woett, there likely was no 1/n in front when Brendan McKay made his comment. There certainly wasn't when I made my earlier comments. Gerhard "However, All Is Better Now" Paseman, 2012.04.17 | |
| Apr 17, 2012 at 17:59 | vote | accept | unknown | ||
| Apr 17, 2012 at 15:24 | comment | added | Woett | @Brandon, look at the $\frac{1}{n}$-term in front | |
| Apr 17, 2012 at 15:17 | answer | added | Emil Jeřábek | timeline score: 19 | |
| Apr 17, 2012 at 15:03 | history | edited | unknown | CC BY-SA 3.0 |
fixing important stuff
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| Apr 17, 2012 at 14:59 | comment | added | Brendan McKay | The $r=2$ term is $\frac12$ for every odd $n$, so how can can the limit be less than $\frac12$? | |
| Apr 17, 2012 at 14:59 | comment | added | unknown | @Igor: thanks for spotting the typo. And no, I cannot prove this, this is purely experimental. | |
| Apr 17, 2012 at 14:57 | comment | added | Gerhard Paseman | Further, I see no way of rescuing the problem without making the denominator substantially bigger, as in r^2 or n^2, or making the numerator correspondingly smaller. Gerhard "Ask Me About System Design" Paseman, 2012.04.17 | |
| Apr 17, 2012 at 14:57 | history | edited | unknown | CC BY-SA 3.0 |
edited body
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| Apr 17, 2012 at 14:56 | comment | added | Igor Rivin | Can the OP prove this, or is this an experimental fact? | |
| Apr 17, 2012 at 14:56 | comment | added | Igor Rivin | The text is incorrect (should be the remainder of $n$ divided by $r$) | |
| Apr 17, 2012 at 14:48 | comment | added | Gerhard Paseman | Without conditions on n, I have a hard time believing that lim inf of the sum is as large as you claim. I do not think the limit exists. Gerhard "Ask Me About System Design" Paseman, 2012.04.17 | |
| Apr 17, 2012 at 14:28 | history | asked | unknown | CC BY-SA 3.0 |