File:Pm1234 means.svg

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Summary

Description
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
Source User created
Author User:Melchoir
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GNU head 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.
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This licensing tag was added to this file as part of the GFDL licensing update.
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic, 2.0 Generic and 1.0 Generic license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
You may select the license of your choice.

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inception

25 February 2007

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Date/TimeThumbnailDimensionsUserComment
current20:04, 12 March 2007Thumbnail for version as of 20:04, 12 March 2007379 × 325 (43 KB)Melchoirknock out border
03:50, 25 February 2007Thumbnail for version as of 03:50, 25 February 2007379 × 325 (43 KB)Melchoirwhoops, screwed up fonts
03:49, 25 February 2007Thumbnail for version as of 03:49, 25 February 2007379 × 328 (308 KB)Melchoirtweak layer order
03:31, 25 February 2007Thumbnail for version as of 03:31, 25 February 2007379 × 325 (43 KB)MelchoirTerms, partial sums, first and second arithmetic means, and (C, 2) sum of the series 1 − 2 + 3 − 4 + · · ·
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