File:Pm1234 means.svg

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Pm1234_means.svg‎ (SVG file, nominally 379 × 325 pixels, file size: 43 KB)

[edit] Summary

Description	Pm1234 means.svg English: Terms, partial sums, first and second arithmetic means, and (H, 2) sum of the series 1 − 2 + 3 − 4 + · · · The horizontal axis is for indices of various sequences associated to the series. The vertical axis is for the values of the terms of those sequences. A term of the series is indicated by the vertical displacement along one of the black diagonal arrows. A partial sum of the series is indicated by an arrowhead. These have values 1, −1, 2, −2, 3, −3, …. The aqua triangle or cone indicates the envelope of the partial sums. A running arithmetic mean of the partial sums of the series is indicated by orange circles. These have values 1, 0, ²⁄₃, 0, ³⁄₅, 0, ⁴⁄₇, …. A running arithmetic mean of the arithmetic means of the partial sums of the series is indicated by purple dots. The purples dots slowly converge towards the green dotted line, which is plotted at 1/4.
Date	2007-02-25
Source	User created
Author	User:Melchoir
Permission (Reusing this image)	See below.
Other versions	PNG version

[edit] Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".

This file is licensed under the Creative Commons Attribution ShareAlike 3.0 License. In short: you are free to share and make derivative works of the file under the conditions that you appropriately attribute it, and that you distribute it only under a license identical to this one. Official license

This licensing tag was added to this file as part of the GFDL licensing update.

This file is licensed under the Creative Commons Attribution ShareAlike 2.5, Attribution ShareAlike 2.0 and Attribution ShareAlike 1.0 License. In short: you are free to share and make derivative works of the file under the conditions that you appropriately attribute it, and that you distribute it only under a license identical to this one.

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File history

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	20:04, 12 March 2007		379×325 (43 KB)	Melchoir (talk \| contribs)	(knock out border)
	03:50, 25 February 2007		379×325 (43 KB)	Melchoir (talk \| contribs)	(whoops, screwed up fonts)
	03:49, 25 February 2007		379×328 (308 KB)	Melchoir (talk \| contribs)	(tweak layer order)
	03:31, 25 February 2007		379×325 (43 KB)	Melchoir (talk \| contribs)	(Terms, partial sums, first and second arithmetic means, and (C, 2) sum of the series 1 − 2 + 3 − 4 + · · ·)