Timeline for Almost binomial sum limit
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 28, 2016 at 6:31 | history | edited | T. Amdeberhan | CC BY-SA 3.0 |
edited body
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| Dec 28, 2016 at 6:30 | comment | added | T. Amdeberhan | Actually, it should be corrected as you said. | |
| Dec 28, 2016 at 6:28 | comment | added | Eugene | One more, the step from 3rd to 4th inequality line : you can improve the estimate to be $(k-1)\binom{n}{k-1}$ if I understood correctly. | |
| Dec 28, 2016 at 6:20 | comment | added | Eugene | Also, I'd like to point out that $t(n-t) \geq n-1$. And that's why you using it in the $\leq$ estimate, b/c $a < 1$. | |
| Dec 28, 2016 at 5:52 | comment | added | T. Amdeberhan | That's correct, and that contribution comes from (i) above; (ii) is smaller. | |
| Dec 28, 2016 at 5:49 | comment | added | Eugene | Also, is it correct that this sum is $1+O(a^{n-1})$? | |
| Dec 28, 2016 at 5:46 | comment | added | T. Amdeberhan | I'm glad to help. | |
| Dec 28, 2016 at 5:44 | history | edited | T. Amdeberhan | CC BY-SA 3.0 |
added 172 characters in body
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| Dec 28, 2016 at 5:44 | vote | accept | Eugene | ||
| Dec 28, 2016 at 5:44 | comment | added | Eugene | I independently obtained the proof for $a < 0.5$ using upper bound for binomials. Your trick completed the task I was struggling with. Thanks! | |
| Dec 28, 2016 at 5:35 | history | answered | T. Amdeberhan | CC BY-SA 3.0 |