\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}