File:Eulergamma.png

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Original file ‎(1,152 × 750 pixels, file size: 39 KB, MIME type: image/png)

Captions

Captions

Graph of the harmonic series H_n and its approximations: Smaller triangles with ln(n+1) demonstrate a closer approximation at lower n, visually representing Euler's constant γ.

Summary[edit]

Description
English: Graphical representation of Riemann sum approximations for the harmonic series. The red and blue curves denote the functions y = 1/x and y = 1/(x+1), respectively, while the purple rectangles underneath the red curve estimate the sum of the series 1/k from k=1 to n.
Date
Source Own work
Author Twoxili

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

File history

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Date/TimeThumbnailDimensionsUserComment
current21:37, 3 May 2024Thumbnail for version as of 21:37, 3 May 20241,152 × 750 (39 KB)Twoxili (talk | contribs)Extended y = 1/(x+1) to x = 0
21:20, 3 May 2024Thumbnail for version as of 21:20, 3 May 20241,152 × 750 (37 KB)Twoxili (talk | contribs)Reverted to using purple rectangles from x = 0 to represent the Riemann sum of y = 1/x from x = 1
21:02, 3 May 2024Thumbnail for version as of 21:02, 3 May 20241,152 × 750 (40 KB)Twoxili (talk | contribs)Aligned onsets of rectangles to those of their respective functions
02:30, 27 April 2024Thumbnail for version as of 02:30, 27 April 20241,152 × 750 (39 KB)Twoxili (talk | contribs)Extended 1/(x+1) curve to x = 0
02:05, 27 April 2024Thumbnail for version as of 02:05, 27 April 20241,152 × 750 (37 KB)Twoxili (talk | contribs)Added lower bound of each function
23:04, 26 April 2024Thumbnail for version as of 23:04, 26 April 20241,152 × 750 (35 KB)Twoxili (talk | contribs)Added x = 0 index to the red and purple boxes
22:37, 26 April 2024Thumbnail for version as of 22:37, 26 April 20241,152 × 750 (35 KB)Twoxili (talk | contribs)Uploaded own work with UploadWizard

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