Image:Pm1234 means.svg

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

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[edit] 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.
Source

User created
Date

2007-02-25
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:
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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File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeDimensionsUserComment
current20:04, 12 March 2007379×325 (43 KB)Melchoir (knock out border)
03:50, 25 February 2007379×325 (43 KB)Melchoir (whoops, screwed up fonts)
03:49, 25 February 2007379×328 (308 KB)Melchoir (tweak layer order)
03:31, 25 February 2007379×325 (43 KB)Melchoir (Terms, partial sums, first and second arithmetic means, and (C, 2) sum of the series 1 − 2 + 3 − 4 + · · ·)
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