Timeline for Limit of partial sums involving inverse squares
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 8, 2020 at 1:49 | answer | added | SonerAlbayrak | timeline score: 1 | |
| Nov 23, 2015 at 1:04 | history | edited | J. M.'s missing motivation♦ | CC BY-SA 3.0 |
deleted 8 characters in body
|
| Oct 8, 2015 at 7:28 | answer | added | J. M.'s missing motivation♦ | timeline score: 5 | |
| Sep 23, 2015 at 6:24 | comment | added | Dr. Wolfgang Hintze | Complete answer (how Mathematica can be used to calculate the limit) now available. See my EDIT #3. | |
| Sep 22, 2015 at 15:29 | comment | added | Daniel Lichtblau | Right, yes, now it's clear. The limit is 1. Showing this using Mathematica is another matter I do not offhand know how to do. | |
| Sep 22, 2015 at 7:29 | answer | added | Dr. Wolfgang Hintze | timeline score: 4 | |
| Sep 21, 2015 at 21:38 | answer | added | Anton Antonov | timeline score: 11 | |
| Sep 21, 2015 at 18:57 | comment | added | Dr. Wolfgang Hintze | Yes, I know that the limit exists. It is a well-know limiting procedure. | |
| Sep 21, 2015 at 16:41 | comment | added | ewcz |
It seems to me that the limit should exist. At least if I fix x>1, then (using the notation of the previous answer) 0<rs[x,n]<=x. Also, for fixed x>1, the sequence rs[x,n] seems to be monotonous (in n) and therefore the limit should exist in this case.
|
|
| Sep 21, 2015 at 15:42 | comment | added | Daniel Lichtblau |
The following suggests that a limit does not exist. Table[Limit[ x/n*Expand[ Sum[Normal[ Series[n^2/(i + (n - i) x)^2, {n, Infinity, j}, Assumptions -> {1 < i < n}]], {i, 1, n}]], n -> Infinity], {j, 1, 6}]. It appears that we have (x^j-(x-1)^j)/x^j as jth term.
|
|
| Sep 21, 2015 at 14:18 | comment | added | MarcoB | But you do know that a finite limit exists? | |
| Sep 21, 2015 at 12:56 | answer | added | user31001 | timeline score: 2 | |
| Sep 21, 2015 at 11:47 | history | asked | Dr. Wolfgang Hintze | CC BY-SA 3.0 |