File:Decision diagram for the ratio test.svg
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Summary
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
\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
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![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)
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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
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- 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.
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15 November 2015
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 18:21, 7 June 2017 | ![]() | 478 × 551 (51 KB) | wikimediacommons>Stephan Kulla | Change \lim to \liminf |
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Width | 382.181pt |
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Height | 440.431pt |