[Tex/LaTex] How to draw infinite earring with TikZ

diagramstikz-pgf

I want to draw an infinite earring, i.e., each circle centerd at $(\frac{1}{n},0)$ with radius $\frac{1}{n}$ for each $n\in \mathbf{N}$. The figure will be the following:

wanted

I have used the following code to do the diagram: 

\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\begin{document}

\begin{tikzpicture} 
  \foreach \n in {1,2,3,4,5,6,7,...................} 
    \draw (1/\n,0) circle (1/\n);
  \foreach \n in {1,2,3,4,5,6,7,...................}  
    \draw[fill] (1\n,0) circle (0.5pt);
\end{tikzpictute}
\end{document}

But it shows an error.

Best Answer

May be better than infinity you fix a large number

 \documentclass{article}
 \usepackage{tikz}
 \begin{document}

 \begin{tikzpicture} 
  \foreach \n in {1,2,...,2000} 
   \draw (1/\n,0) circle (1/\n);
 \end{tikzpicture}
 \end{document}

Edit: we can replace

  \foreach \n in {1,2,...,2000}

by

  \foreach \n in {1,...,2000}

since the step is 1

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