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\begin{document}
On considère la fonction $1$-périodique $f \colon \mathbb{R}\to \mathbb{R}$ déterminée par :\\[1mm]
\hspace*{\fill}
$f(x) = \fontsize{10}{10}\selectfont
\left\{\begin{array}{cl}
-1&\text{ si } x \in \left]-\frac{1}{2},0\right] \\[0.5mm]
1&\text{ si } x \in \left]0,\frac{1}{2}\right]
\end{array}\right.$.
\hspace*{\fill}\par\medskip
Voici les tracés des graphes des applications $S_{2n-1}(f)$ :
\par\vskip5mm\hspace*{\fill}
\psset{unit=7cm,algebraic=true}%
\begin{pspicture}(-0.55,-1.25)(0.65,1.325)
\psaxes[ticks=none,labels=none,arrowscale=1.5]{->}(0,0)(-0.55,-1.25)(0.6,1.3)[$x$,-90][$y$,180]
\uput[dl](0,0){$O$}
\def\f{0}
\multido{\n=1+1}{5}{%
\edef\f{\f+4/PI*sin((2*\n-1)*2*PI*x)/(2*\n-1)}%
\ifnum\n=1\psplot[linecolor=cyan,plotpoints=100]{-0.5}{0.5}{\f}\fi
\ifnum\n=2\psplot[linecolor=orange,plotpoints=200]{-0.5}{0.5}{\f}\fi
\ifnum\n=3\psplot[linecolor=green,plotpoints=300]{-0.5}{0.5}{\f}\fi
\ifnum\n=4\psplot[linecolor=yellow,plotpoints=400]{-0.5}{0.5}{\f}\fi
\ifnum\n=5\psplot[linecolor=magenta,plotpoints=500]{-0.5}{0.5}{\f}\fi
}
\uput[d](-0.3,0.8){\parbox{2.4cm}{valeurs de $n$ :\\
\color{cyan} 1, \color{orange} 2, \color{green} 3, \color{yellow} 4, \color{magenta} 5}}
\end{pspicture}\hspace*{\fill}
\end{document}