Wikimedia Commons

File:PartialGeometricSums.jpg

PartialGeometricSums.jpg ‎(369 × 280 pixels, file size: 25 KB, MIME type: image/jpeg)

Captions

Captions

Add a one-line explanation of what this file represents

Summary

edit
Description
English: Partial geometric sums for the geometric series Σimi, summed over i=0,1,2,...n, are tracked using arrows for n from 1 to 4 on this inverse stereographic projection of the real manifold: in cyan for m = ½, blue for m = 2, red for m = -2, and chartreuse for m = -½.

The distributivity-based asymptotic solutions (using Σ = 1+mΣ) for the sum to n = infinity are shown with open circles: at Σ ~ 2 (cyan) for m = ½, at Σ ~ -1 (blue) for m = 2, at Σ ~ 1/3 (red) for m = -2, and at Σ ~ 2/3 (chartreuse) for m = -½.

As is graphically obvious, the partial sums only converge to the associated infinite sum (open circle of the same color) when Abs[m] < 1.
Date
Source Own work
Author P. Fraundorf

Licensing

edit
I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International 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.

File history

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

Date/TimeThumbnailDimensionsUserComment
current13:07, 23 August 2016Thumbnail for version as of 13:07, 23 August 2016369 × 280 (25 KB)Unitsphere (talk | contribs)User created page with UploadWizard

You cannot overwrite this file.

There are no pages that use this file.

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:PartialGeometricSums.jpg&oldid=499055643"