可视化序列的收敛

Question

我希望以类似于维基百科下图的方式可视化序列的收敛：

有人能帮我用 Tikz 画一幅类似的画吗？非常感谢！

Answer 1

画出这样的东西很容易，因为 Ti钾Z 解析其表达式。

\documentclass[tikz,border=3mm]{standalone}
\begin{document}
\begin{tikzpicture}
 \draw[stealth-stealth] (0,5) |- (8,0) node[right]{$n$};
 \pgfmathsetseed{7}
 \draw plot[variable=\x,samples at={0.3,0.6,...,2.4,3.3,3.7,...,8},only marks,mark=*,
    mark options={blue}] (\x,{2+2*sin(360*rnd)*exp(-0.25*\x)});
 \draw[densely dashed] (0,2) -- (8,2) node[right]{$a$}; 
 \draw(3,2) circle[x radius=0.4,y radius=1];
 \fill[red] (2.7,3.1)   circle[radius=2pt];
 \fill[green!70!black] (3,1.1)  circle[radius=2pt];
 \draw[green!70!black,latex-] (3,1) -- ++(0,-0.3) node[below]{$a_{N_0}$};
 \draw (3,0.1) -- (3,-0.1) node[below]{$N_0$};
 \foreach \X in {+,-}
  {\draw (3,2\X 1) -- (8,2\X 1) node[right]{$a\X\varepsilon$};}
\end{tikzpicture}
\end{document}