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+\input{exercises.tex} +\printcollection{banque} +\vfill +\printcollection{banque} + +\end{document} diff --git a/TST/09_Somme_suites/exercises.tex b/TST/09_Somme_suites/exercises.tex index bb72d58..e0b51eb 100644 --- a/TST/09_Somme_suites/exercises.tex +++ b/TST/09_Somme_suites/exercises.tex @@ -31,14 +31,44 @@ \paragraph{Barème} \begin{itemize} \item (raisonner) Pertinence des questions posées \dotfill 1pt - \item (communiquer) Clarté des explications \dotfill 2pts + \item (communiquer) Clarté des explications \dotfill 1pt \item (modélisation) Choix des outils mathématiques utilisés\dotfill 1pt \item (représenter) Schémas pour illustrer \dotfill 1pt \item (raisonner) Rigueur des explications apportés \dotfill 1pt \item (calculs) Justesse des calculs \dotfill 2pts \item (représenter) Graphiques des évolutions \dotfill 1pt \item (communiquer) Description des évolutions \dotfill 1pt + \item (communiquer) Algorithmes \dotfill 1pt \end{itemize} \end{exercise} +\begin{exercise}[subtitle={Technique}, step={2}, origin={Créations}, topics={Somme suites}, tags={Suites, analyse}] + Expliciter puis calculer la somme $\ds \sum_{n=0}^{20}u_n$ pour les suites suivantes + \begin{enumerate} + \item $(u_n)$ arithmétique de raison $r=3$ et de premier terme $u_0 = 1$ + \item $(u_n)$ arithmétique de raison $r=-2$ et de premier terme $u_0 = 50$ + \item $(u_n)$ géométrique de raison $q=1.5$ et de premier terme $u_0 = 10$ + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Consommation de cigarettes}, step={2}, origin={Créations}, topics={Somme suites}, tags={Suites, analyse}] + Bob décide d'arrêter de fumer au premier janvier. Il décide de le faire progressivement. Il sait qu'il consomme 140 cigarettes par semaine. Il souhaite alors partir de ce point la première semaine puis de diminuer chaque semaine de 20 cigarettes. On note $(u_n)$ le nombre de cigarette que Bob projeté de fumer par semaine. + \begin{enumerate} + \item Quelle est la nature de la suite $(u_n)$? Préciser ses paramètres. Expliciter la formule de récurrence et la formule explicite. + \item Combien de temps faudra-il à Bob pour arrêter de fumer? + \item Combien de cigarettes aura-t-il fumé en tout depuis qu'il aura décidé d'arrêter? + \item Écrire une algorithme qui calcule le nombre total de cigarettes fumées. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Mégot de cigarettes}, step={2}, origin={Créations}, topics={Somme suites}, tags={Suites, analyse}] + Pour rendre sa ville plus agréable et lutter contre les mégots jetés par terre. Le maire d'une commune dépose un arrêté prévoyant une amende de 160\euro en cas de flagrant délie. Cette mesure est sensé faire diminuer le nombre de mégots jetés par terre de 15\% par an. Il était temps, en 2019, les agents publiques en avait ramassé \np{20000}. + + \begin{enumerate} + \item On note $(u_n)$ la suite modélisant le nombre de mégots jeté par terre en 1 ans à partir de l'année 2019. Décrire la suite $(u_n)$. + \item Combien d'années faudra-t-il attendre pour que le nombre de mégots jetés par an passent en dessous de 100. + \item Combien de mégots auront été alors jeté depuis la mise en place de l'arrêté? + \item Proposer une algorithme qui calculer le nombre total de mégots jeté jusqu'à ce que le nombre de mégots jetés par an passe en dessous de 100. + \end{enumerate} +\end{exercise} \collectexercisesstop{banque} diff --git a/TST/09_Somme_suites/index.rst b/TST/09_Somme_suites/index.rst index b9527a8..3d5657c 100644 --- a/TST/09_Somme_suites/index.rst +++ b/TST/09_Somme_suites/index.rst @@ -37,6 +37,10 @@ Bilan: algorithme d'accumulations et symbole somme Exercices techniques pour calculer des sommes de termes. +.. image:: ./3E_somme.pdf + :height: 200px + :alt: Exercices sur les sommes de suites + Étape 3: Exercices bilan sur les suites =======================================