Timeline for Another limit involving the fractional part
Current License: CC BY-SA 4.0
6 events
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| Apr 6 at 3:45 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Apr 5 at 5:43 | vote | accept | Babar | ||
| Apr 5 at 5:43 | comment | added | Babar | Thanks again! Great answer. In the meantime, I think I managed to find the limit by writing $f(x)=\frac{1-\left|2\left\{ {x}\right\} -1\right|}{2}$ and using after justification (to be rigorously demonstrated) $\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{k=1}^{n}f\left(\frac{n}{k }\right)=\int_{0} ^{1}f(1/t)dt$ with change of variable $u=1/t$ and splitting the integral over the intervals $]k,k+1] $. But that doesn't give the error term.... | |
| Apr 4 at 23:06 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Apr 4 at 23:01 | history | edited | GH from MO | CC BY-SA 4.0 |
added 109 characters in body
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| Apr 4 at 22:56 | history | answered | GH from MO | CC BY-SA 4.0 |