From 4875a4cd8ce047c4c7788ccea2646ddaf0377d09 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Thu, 8 Oct 2020 09:45:37 +0200 Subject: [PATCH 1/2] =?UTF-8?q?Feat:=20=C3=A9tape=201=20sur=20la=20formali?= =?UTF-8?q?sation=20des=20suites?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../1B_formalisation.pdf | Bin 0 -> 59717 bytes .../1B_formalisation.tex | 111 +++++++++++++++++- .../1E_formalisation.pdf | Bin 57756 -> 70165 bytes .../1E_formalisation.tex | 3 + TST/04_Formalisation_des_suites/exercises.tex | 27 ++++- TST/04_Formalisation_des_suites/index.rst | 8 ++ 6 files changed, 141 insertions(+), 8 deletions(-) create mode 100644 TST/04_Formalisation_des_suites/1B_formalisation.pdf diff --git a/TST/04_Formalisation_des_suites/1B_formalisation.pdf b/TST/04_Formalisation_des_suites/1B_formalisation.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8e9c2cb6db4cb54c8cc65760e8f40411e8f2b0df GIT binary patch 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ze2HKf|Kev#@&}Q&Bv*vgqPZKBxxOaE1zPRzZJT#AAiuJBVTpbGm91_0_Syov?4~s3 zPkx%u?_(qB_WVMy+Dk1(_;{r8(lRHk7*FxGIo96nKaTx}nVg}] (premier.east) edge [bend left] node [above] {$+r$} (deuxieme.west); + \path[->] (deuxieme.east) edge [bend left] node [above] {$+r$} (troisieme.west); + \path (troisieme.east) node [right] {....} (ad.west); + \path[->] (ad.east) edge [bend left] node [above] {$+r$} (der.west); + \end{tikzpicture} + \end{center} + La quantité ajoutée $r$ est appelée la \textbf{raison}. + + \columnbreak + Une suite géométrique modélise les situations où l'on répète une \textbf{multiplication}. + \begin{center} + \begin{tikzpicture}[ + roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm}, + ] + %Nodes + \node[roundnode] (premier) {\makebox[0.5cm]{$u_0$}}; + \node[roundnode] (deuxieme) [right=of premier] {\makebox[0.5cm]{$u_1$}}; + \node[roundnode] (troisieme) [right=of deuxieme] {\makebox[0.5cm]{$u_2$}}; + \node[roundnode] (ad) [right=of troisieme] {\makebox[0.5cm]{$u_n$}}; + \node[roundnode] (der) [right=of ad] {\makebox[0.5cm]{$u_{n+1}$}}; + + %Lines + \path[->] (premier.east) edge [bend left] node [above] {$\times q$} (deuxieme.west); + \path[->] (deuxieme.east) edge [bend left] node [above] {$\times q$} (troisieme.west); + \path (troisieme.east) node [right] {....} (ad.west); + \path[->] (ad.east) edge [bend left] node [above] {$\times q$} (der.west); + \end{tikzpicture} + \end{center} + La quantité par laquelle on multiplie $q$ est appelée la \textbf{raison}. +\end{multicols} + +\subsection*{Formules de récurrence} +\begin{multicols}{2} + \[ + u_{n+1} = u_{n} + r + \] + \columnbreak + \[ + u_{n+1} = u_{n} \times q + \] +\end{multicols} + +\subsection*{Formules explicite} +\begin{multicols}{2} + \[ + u_{n} = u_{0} + r\times n + \] + \columnbreak + \[ + u_{n} = u_{0} \times q^n + \] +\end{multicols} +\subsection*{Déterminer la nature d'une suite} +\begin{multicols}{2} + On calcule la \textbf{différence} entre deux termes consécutifs. Le résultat doit être toujours le même et ne pas dépendre de $n$. + \[ + u_1 - u_0 = ... + \] + \[ + u_2 - u_3 = ... + \] + Ou plus généralement, + \[ + u_{n+1} - u_n = ... + \] + + + \columnbreak + + On calcule la \textbf{quotient} entre deux termes consécutifs. Le résultat doit être toujours le même et ne pas dépendre de $n$. + \[ + \frac{u_1}{u_0} = ... + \] + \[ + \frac{u_2}{u_3} = ... + \] + Ou plus généralement, + \[ + \frac{u_{n+1}}{u_n} = ... + \] +\end{multicols} + +\end{document} diff --git a/TST/04_Formalisation_des_suites/1E_formalisation.pdf b/TST/04_Formalisation_des_suites/1E_formalisation.pdf index f6990dfd25b002979d076f90fc3b7294b0747341..34961cd2fc9cbbb0ab9c9ea42da7a7bdec3b91df 100644 GIT binary patch delta 48415 zcmZU)Q*@vW&~6#4W81cEqvNDw+cw_Vw(X8O=-5s=wr$(V`ObgN%v{Xfb5pA>YgesZ zIRoISB@p#&P*|+Q%)}1H)^Pm%a7;hV>@8d^iCI~AIFpSasDVpuo%r>?sQ%jqBnO4S^$(?SaTG~pdVmDS*(3U2r*CbA1{xK-}bfooqMdL5EP;_Cr8T>)`JC7 zCSf6zvy=SZY=GA*OPOtwopBLmqc7%!45nfwDH`gx^F6}_eaZnYW?Brh*5_Kyd${3s zI+q4fZ2<0z6e-xc(d6Y{S*gau#cTsd_V7OryLf3QCtQ3kI4qP2th(aSC*{A17>78q zP?d?B`kvESc9YfrOhlt*wBVs43F42%oA7)Xc@j zG_&Sn)53ze7VDQ)8~Wgj_=;Brr`mizS-!qCn$?b|glSbi&oB(kQ;}{5JhgDYS8H8G^Ac)XXiryRr zd>Px;_KziuV9^kS{>1KL8O8!eXv-pteV8Rb@xITb^wLuZHxl+!@FZUO@6+00lyZ!x 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À partir de deux termes + nature ou de 3 termes retrouver u0 et la raison. +.. image:: ./2E_technique.pdf + :height: 200px + :alt: Exercices techniques pour retrouver la raison et le premier terme. + + Étape 3: Moyenne arithmétique et géométrique ============================================ @@ -40,4 +45,7 @@ Questions d'intro puis cours puis exercices techniques. Type E3C - +Exercices à revoir mais sympa: +- MATH2T-122A0-1125 (avec graph exponentiel) +- MATH2T-122A0-1130 (avec formule explicite) +- MATH2T-123A0-1126 (formule puis modélisation)