File:Pm1234 means.png
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Summary
editTerms, 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.
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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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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current | 17:36, 13 March 2007 | ![]() | 1,516 × 1,300 (89 KB) | Melchoir (talk | contribs) | == Summary == 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 vert |
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