File:Decision diagram for the ratio test.svg

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Summary

Description
English: Decision diagram for the ratio test
Date
Source Own work
Author Stephan Kulla (User:Stephan Kulla)
Other versions

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

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
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You are free:
  • to share – to copy, distribute and transmit the work
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15 November 2015

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Date/TimeThumbnailDimensionsUserComment
current03:21, 7 June 2017Thumbnail for version as of 03:21, 7 June 2017478 × 551 (51 KB)Stephan KullaChange \lim to \liminf

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