chapitres 1ere et 2nde
authorDenise sur Lya <sekhmet@lya>
Wed, 18 May 2016 10:56:16 +0000 (12:56 +0200)
committerDenise sur Lya <sekhmet@lya>
Wed, 18 May 2016 10:56:16 +0000 (12:56 +0200)
1ere/chapitre7_suites/chap7.pdf
1ere/chapitre7_suites/chap7.tex
1ere/chapitre7_suites/fondgraphique2.pdf [new file with mode: 0644]
1ere/chapitre7_suites/fondgraphique2.svg [new file with mode: 0644]
2nde/chapitre10_vecteurs/chap10.pdf
2nde/chapitre10_vecteurs/chap10.tex

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@@ -187,7 +187,91 @@ Pour une suite arithmétique $(u_n)$, la \souligne{variation absolue} ~ $u_{n+1}
 
 Vocabulaire : on dit que l'évolution est \ldots \ldots \ldots \ldots
 \end{prop}
+
+%%%
 \section{Suites géométriques}
 
 
+
+\subsection{Définition et premières propriétés}
+
+\begin{defn}
+Une suite $(u_n)$ est dite \souligne{géométrique} lorsque \dotfill
+
+\smallskip
+
+\lignepoint
+
+\smallskip
+
+\lignepoint
+\end{defn}
+
+\bigskip
+
+Exemple : $(u_n)$ définie par $u_0 = 2$ et $u_{n+1} = 3u_n $ est \dotfill
+
+\lignepoint
+
+\smallskip
+
+$(v_n)$ avec $v_0 = 100$ et $v_{n+1}$ est $v_n$ augmenté de \upc{10} : \dotfill
+
+\lignepoint
+
+
+\bigskip
+
+\begin{prop}
+Le terme général d'une suite géométrique $(u_n)$ de premier terme $u_0$ et de raison $q$ est
+
+\vspace{1cm}
+\end{prop}
+
+\bigskip
+
+\souligne{Remarque}~: si le premier terme est $u_1$, on a \dotfill
+
+
+\bigskip
+
+Exemple : dans les exemples ci-dessus, on a \dotfill
+
+\smallskip
+
+\lignepoint
+
+\subsection{Variations}
+
+\begin{prop}
+Soit $q>0$, et $(u_n)$ la suite de terme général $u_n = q^n$.
+\begin{itemize2}
+\item Si $q>1$, la suite $(u_n)$ est \ldots \ldots \ldots 
+\item Si $q<1$, la suite $(u_n)$ est \ldots \ldots \ldots 
+\item Si $q=1$, la suite $(u_n)$ est \ldots \ldots \ldots 
+\end{itemize2}
+\end{prop}
+
+Exemples :
+
+
+%\newcommand\bli{p{3.3cm}}
+\noindent\begin{minipage}{11cm}
+\noindent\begin{tabular}{\bli|\bli|\bli}
+\vspace{3cm} &~ & ~ \\
+\end{tabular}
+\end{minipage}
+\begin{minipage}{5cm}
+\includegraphics[width=5cm]{fondgraphique2.pdf}
+\end{minipage}
+
+\begin{prop}
+Pour une suite arithmétique $(u_n)$, la \souligne{variation relative} ~ $\frac{u_{n+1} - u_n}{u_n}$ est \ldots \ldots \ldots \ldots
+
+\bigskip
+
+Vocabulaire : on dit que l'évolution est \ldots \ldots \ldots \ldots
+\end{prop}
+
+
 \end{document}
diff --git a/1ere/chapitre7_suites/fondgraphique2.pdf b/1ere/chapitre7_suites/fondgraphique2.pdf
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index b983cef..cabac11 100644 (file)
Binary files a/2nde/chapitre10_vecteurs/chap10.pdf and b/2nde/chapitre10_vecteurs/chap10.pdf differ
index 06fa01b..67bf4db 100644 (file)
@@ -185,4 +185,91 @@ $\vw = -1,5 \vu$
 \end{minipage}\begin{minipage}{7cm}
 \includegraphics[width=7cm]{grille.png}
 \end{minipage}
+\newpage
+
+\begin{prop}
+Pour tous vecteurs $\vu$, $\vv$ et tous nombres réels $k$ et $k'$ :
+\begin{itemize2}
+\item $(k+k')\vu = \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots $
+\item $k(\vu + \vv) = \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$
+\item $k(k'\vu) = \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$
+\end{itemize2}
+\end{prop}
+
+\smallskip
+
+Exemples : 
+\[-2(7\vu -4\vu) + 5\vu = \hspace{10cm} \]
+\[\ve{AB} + 3(\ve{BA} + 7CD) = \hspace{10cm} \]
+
+\bigskip
+
+\begin{defn}
+Deux vecteurs $\vu$ et $\vv$ sont dits \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots  \ldots \ldots \ldots \ldots \ldots s'il existe un réel $k$ tel que $\vv = k\vu$ ou un réel $k'$ tel que $\vu = k\vv$.
+\end{defn}
+
+\bigskip
+
+Remarque : $0 \times \vu = $\dotfill
+
+\bigskip
+
+Exemple :
+$\vu(-4; 1)$ et $\vv\left(2; -\frac{1}{2}\right)$ \dotfill
+
+\smallskip
+
+\lignepoint
+
+\smallskip
+
+\lignepoint
+
+\smallskip
+
+\lignepoint
+\bigskip
+
+\begin{thm}
+Soient $A$, $B$ et $C$ trois points du plan. $A$, $B$ et $C$ sont alignés si et seulement si 
+\lignepoint
+\end{thm}
+
+\bigskip
+
+Exemple : $A(-2; 3)$, $B(1, 1)$ et $C(2; 2)$ sont-ils alignés ?
+
+\begin{minipage}{10cm}
+\lignepoint
+\lignepoint
+\lignepoint
+\lignepoint
+\lignepoint
+\lignepoint
+\end{minipage}\begin{minipage}{7cm}
+\includegraphics[width=7cm]{grille.png}
+\end{minipage}
+
+\bigskip
+
+\begin{thm}
+Soient $A$, $B$, $C$, $D$ quatre points du plan, deux à deux distincts. Les droites $(AB)$ et $(CD)$ sont parallèles si et seulement si \dotfill
+\end{thm}
+
+\bigskip
+
+Exemple : Aux points de l'exemple précédent, on rajoute $D\left( \frac{13}{2}; -1 \right)$. Les droites $(AB)$ et $(CD)$ sont-elles parallèles ?
+
+\begin{minipage}{10cm}
+\lignepoint
+\lignepoint
+\lignepoint
+\lignepoint
+\lignepoint
+\lignepoint
+\end{minipage}\begin{minipage}{7cm}
+\includegraphics[width=7cm]{grille.png}
+\end{minipage}
+
+%%
 \end{document}