Timeline for An elementary proof for a limit?
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Oct 2, 2016 at 6:14 | comment | added | Fedor Petrov | @T.Amdeberhan you are not right, this sequence does not satisfy $a_n-a_{n-1}=O(1/n^2)$, you maybe forgot that $n$ is different for $a_n$ and for $a_{n-1}$. Of course a series $\sum c_n$ converges if $c_n=O(1/n^2)$. | |
| Oct 2, 2016 at 2:12 | comment | added | T. Amdeberhan | I'm not sure we can say $a_n-a_{n-1}=O(1/n^2)$ implies $a_n$ converges, in general. Take $a_n=\log(n^2)$ for $n$ even; $a_n=\log(1+n^2)$ for $n$ odd. Am I right? We need to follow through Fedor's argument on the series $\sum (a_{n-1}-a_n)$. | |
| Oct 1, 2016 at 22:55 | history | answered | Vladimir Dotsenko | CC BY-SA 3.0 |