Timeline for asymptotic behaviour of a sum
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 4, 2012 at 10:27 | vote | accept | user22980 | ||
| Jun 4, 2012 at 5:40 | history | edited | Alex Becker | CC BY-SA 3.0 |
added 3 characters in body
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| Jun 3, 2012 at 8:26 | comment | added | user22980 | One last mistake: in making the first approximations you forgot the $4$ that multiply $N^2 x^2$. So the correct function $f$ is: $$f(x)=\frac{2+x^2−x\sqrt{4+x^2}}{4}$$ I made a plot and now it works! | |
| Jun 3, 2012 at 3:49 | history | edited | Alex Becker | CC BY-SA 3.0 |
deleted 2 characters in body
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| Jun 3, 2012 at 3:40 | comment | added | fedja | @Alex It's getting late for sure (sigh). Look at your computation again and correct $f(x)$ to the value I posted. Also you have some mysterious $f(x)-2$ instead of $-f(x)$ in the last line before the final "thus". It would be nice to clean that up as well. | |
| Jun 3, 2012 at 3:17 | history | edited | Alex Becker | CC BY-SA 3.0 |
mistake fixed
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| Jun 3, 2012 at 3:04 | comment | added | Alex Becker | @fedja Some strange corner of my imagination no doubt. Editing to fix. | |
| Jun 3, 2012 at 2:37 | comment | added | fedja | And where exactly did the power $2k-2-N$ in the numerator come from? I thought we were comparing $k$ to $k+1$, not to $k-1$... | |
| Jun 2, 2012 at 23:53 | comment | added | Alex Becker | @fedja I'm not seeing the error. Since $$\frac{(\sqrt{2}x)^{2k-2-N}}{(\sqrt{2}x)^{2k-N}}=\frac{1}{2x^2}$$ isn't the $2x^2$ on the correct side? | |
| Jun 2, 2012 at 23:33 | comment | added | fedja | It should actually be $f(x)=\frac{2+x^2-\sqrt{x^4+4x^2}}4$ (the factor $2x^2$ went to the wrong side). Other than that, it's correct. | |
| Jun 2, 2012 at 20:53 | comment | added | Alex Becker | It is very possible I made a computational error (or in the case of solving for the optimal $k$, a Mathematica error) in the lengthy string of computations. I hope it doesn't sink things! | |
| Jun 2, 2012 at 20:51 | comment | added | user22980 | Thanks a lot! The idea seems to work, I made a plot and your result is quite different from the real limit: I shall check the computations.. I'll let you know | |
| Jun 2, 2012 at 19:52 | history | edited | Alex Becker | CC BY-SA 3.0 |
signs
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| Jun 2, 2012 at 19:31 | history | answered | Alex Becker | CC BY-SA 3.0 |