File:Decision diagram for the ratio test.svg
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
![File:Decision diagram for the ratio test.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Decision_diagram_for_the_ratio_test.svg/478px-Decision_diagram_for_the_ratio_test.svg.png?20170607092125)
Size of this PNG preview of this SVG file: 478 × 551 pixels. Other resolutions: 208 × 240 pixels | 416 × 480 pixels | 666 × 768 pixels | 888 × 1,024 pixels | 1,777 × 2,048 pixels.
Original file (SVG file, nominally 478 × 551 pixels, file size: 51 KB)
File information
Structured data
Captions
Captions
Add a one-line explanation of what this file represents
Summary
[edit]DescriptionDecision diagram for the ratio test.svg |
English: Decision diagram for the ratio test |
Date | |
Source | Own work |
Author | Stephan Kulla (Stephan Kulla) |
Other versions |
|
SVG development InfoField |
Source code
[edit]\documentclass[border=10pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows}
\everymath{\displaystyle}
\begin{document}
\tikzstyle{decision} = [diamond, draw, fill=yellow!20,
aspect=2, text badly centered, inner sep=0pt]
\tikzstyle{block} = [rectangle, draw, fill=blue!20,
text centered, rounded corners]
\tikzstyle{convergence} = [rectangle, draw, fill=green!20,
node distance=8cm, text centered, rounded corners]
\tikzstyle{divergence} = [rectangle, draw, fill=red!20,
node distance=8cm, text centered, rounded corners]
\tikzstyle{line} = [-stealth, thick, draw]
\begin{tikzpicture}[node distance=4cm, auto, text width=12em]
\node [block] (init) {Calculate $\left|\frac{a_{k+1}}{a_k}\right|$};
\node [decision, below of=init, node distance=3cm] (case1) {Is $\limsup_{k\to\infty} \left|\frac{a_{k+1}}{a_k}\right| < 1$?};
\node [decision, below of=case1] (case2) {Is $\liminf_{k\to\infty} \left|\frac{a_{k+1}}{a_k}\right| > 1$?};
\node [decision, below of=case2] (case3) {Is $\left|\frac{a_{k+1}}{a_k}\right| \ge 1$ for almost all $k\in\mathbb N$?};
\node [convergence, right of=case1] (yes1) {$\sum_{k=1}^\infty a_k$ converges absolutely};
\node [divergence, right of=case2] (no2) {$\sum_{k=1}^\infty a_k$ diverges};
\node [divergence, right of=case3] (no3) {$\sum_{k=1}^\infty a_k$ diverges};
\node [block, below of=case3, node distance=3.5cm] (final) {The ratio test cannot be applied};
\path [line] (init) edge (case1);
\path [line] (case1) -- node [xshift=5em] {Yes} (yes1);
\path [line] (case2) -- node [xshift=5em] {Yes} (no2);
\path [line] (case3) -- node [xshift=5em] {Yes} (no3);
\path [line] (case1) -- node {No} (case2);
\path [line] (case2) -- node {No} (case3);
\path [line] (case3) -- node {No} (final);
\end{tikzpicture}
\end{document}
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
![w:en:Creative Commons](https://upload.wikimedia.org/wikipedia/commons/thumb/7/79/CC_some_rights_reserved.svg/90px-CC_some_rights_reserved.svg.png)
![attribution](https://upload.wikimedia.org/wikipedia/commons/thumb/1/11/Cc-by_new_white.svg/24px-Cc-by_new_white.svg.png)
![share alike](https://upload.wikimedia.org/wikipedia/commons/thumb/d/df/Cc-sa_white.svg/24px-Cc-sa_white.svg.png)
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/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 09:21, 7 June 2017 | ![]() | 478 × 551 (51 KB) | Stephan Kulla (talk | contribs) | Change \lim to \liminf |
18:02, 10 January 2016 | ![]() | 478 × 551 (51 KB) | Stephan Kulla (talk | contribs) | typo | |
17:53, 10 January 2016 | ![]() | 478 × 551 (51 KB) | Stephan Kulla (talk | contribs) | Reverted to version as of 17:37, 15 November 2015 (UTC) | |
17:52, 10 January 2016 | No thumbnail | 0 × 0 (14 KB) | Stephan Kulla (talk | contribs) | typo | |
17:37, 15 November 2015 | ![]() | 478 × 551 (51 KB) | Stephan Kulla (talk | contribs) | User created page with UploadWizard |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
File usage on other wikis
The following other wikis use this file:
- Usage on ar.wikipedia.org
- Usage on de.wikibooks.org
- Usage on en.wikipedia.org
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.
Width | 382.181pt |
---|---|
Height | 440.431pt |