Math & Science ⇒ Illustration of a mathematical progression

[Atticus_Freeze]

I want to know how to make an illustration that plots a sequence such as ${a_n} = 1/n^2$, where n is a natural number, using either pstricks or tikZ. I don't want to use Mathematica or Maple to do this since I want to heavily customize my diagram with specific labels and markers to illustrate the idea of a convergent sequence in real analysis. Any help would be deeply appeciated!!

[frederic]

One possibility is as follows:

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\begin{tikzpicture}[xscale=0.5,yscale=4]
\draw[->] (0,0) -- (10,0) node[right] {$x$};
\draw[->] (0,0) -- (0,1) node[left] {$y$};

\foreach \n [evaluate=\n as \y using 1/\n^2] in {1,...,10}{
  \node at (\n,\y) {\tikz{\fill[blue] (0,0) circle[radius=1pt];}};
}

\end{tikzpicture}

I drew the dots within the nodes, this way they are not affected by the scaling factors of the beginning of the picture. To see this, replace the line with the node by simply

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\fill[blue] (\n,\y) circle[radius=1pt];

Note that this sequence is not a very nice sequence to draw, as it converges rather quickly to 0.

[torbjorn t.]

You could also write it as

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\begin{tikzpicture}[xscale=0.5,yscale=4]
\draw[->] (0,0) -- (10,0) node[right] {$x$};
\draw[->] (0,0) -- (0,1) node[left] {$y$};

\foreach \n [evaluate=\n as \y using 1/\n^2] in {1,...,10}{
  \node at (\n,\y) [fill=blue,circle,inner sep=0pt,minimum size=1pt] {};
}

\end{tikzpicture}

Another possibility using pgfplots:

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\documentclass[a4paper]{article}
\usepackage{tikz,pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
\begin{axis}[samples at={1,2,...,10},ymin=0]
  \addplot+[only marks,mark size=1pt] {1/x^2};
\end{axis}
\end{tikzpicture}
\end{document}

[Atticus_Freeze]

Thank you very much, both of you. Also, 1/n^2, wasn't a good choice. I picked it hastily, but really, I just wanted an example for any convergent sequence. Thanks alot!