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%%%>
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\begin{document}
\title[Séries entières]
\subtitle{Premiers exemples}
\author[ MSAAD]{}
\institute[Institut]{}
\date[11/2019]{}
\maketitle
\begin{frame}
\begin{frame}
\frametitle{Séries entières}
\begin{itemize}
\item \textbf {\textcolor {vert}{Définition : }}
On appelle série entière, toute série de fonctions de la forme $\displaystyle\sum a_nz^n$ où $(a_n)_n\in\mathbb{C}^{\mathbb{N}}$
\end{frame}
\begin{frame}
\frametitle{Lemme d'Abel}
\textbf {\textcolor {vert}{Proposition : }}
Soit $\sum a_nz^n$ une série entière et $z_0\mathbb{C}$ tel que la suite $(a_n)_n$ soit bornée, alors la série $\sum a_nz^n$ converge pour tout nombre complexe $z$ tel que
$\vert z\vert \< \vert z_0\vert$
\end{frame}
\begin{frame}
\frametitle{Lemme d'Abel }
\textbf {\textcolor {vert}{Proposition : }}
Soit $\sum a_nz^n$ une série entière et $z_0\mathbb{C}$ tel que la suite $(a_n)_n$ soit bornée, alors la série $\sum a_nz^n$ converge pour tout nombre complexe $z$ tel que
$\vert z\vert \< \vert z_0\vert$
\end{frame}
\end{document}
