{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Algorithmique : suites"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On considère l'algorithme :  \n",
    "<p style=\"text-align:left; background: lightyellow ; border: 1px solid #999; margin: 10px 0 ; padding: 10px ; width:50% ; \">\n",
    "$n \\leftarrow 0$  <br>\n",
    "$u \\leftarrow 5$   <br>\n",
    "Tant que $n < 4$    <br>\n",
    "    $\\qquad u \\leftarrow u \\times 3 + 2$   <br>\n",
    "    $\\qquad n \\leftarrow n+1$   <br>\n",
    "</p>\n",
    "\n",
    "Quelle est la valeur de la variable $u$ à la fin ? de $n$ ? (vous pouvez le traduire en Python ci-dessous pour vérifier)  \n",
    "\n",
    "*Réponse : $\\dots$*\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On considère l'algorithme :\n",
    "\n",
    "<p style=\"text-align:left; background: lightyellow ; border: 1px solid #999; margin: 10px 0 ; padding: 10px ; width:50%\">\n",
    "$n \\leftarrow 1$   <br>\n",
    "$S \\leftarrow 0$   <br>\n",
    "Tant que $n <5$   <br>\n",
    "    $\\qquad S \\leftarrow S + \\dfrac{1}{n}$   <br>\n",
    "    $\\qquad n \\leftarrow n+1$  <br>\n",
    "</p>\n",
    "\n",
    "\n",
    "Quelle est la valeur de la variable $S$ à la fin ? (vous pouvez le traduire en Python ci-dessous pour vérifier)  \n",
    "\n",
    "*Réponse : $\\dots$*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ecrire un programme qui calcule les 10 premiers termes de la suite $(u_n)$ définie par $u_0 = 0.1$ et, pour tout entier naturel $n$,  $u_{n+1} = 5u_n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour la suite précédente, écrire un programme qui calcule la somme des 10 premiers termes : $u_0+u_1+u_2+ \\dots + u_{9}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On considère la suite $(v_n)$ définie par $v_0 = 500$ et, pour tout entier naturel $n$,  $v_{n+1} = \\sqrt{v_n + 2}$.  \n",
    "Calculer $v_{1}$, $v_{5}$, $v_{10}$. Qu'observe-t-on ?\n",
    "\n",
    "*Réponse : *  $v_1 = \\qquad \\qquad$ ; $v_5 = \\qquad \\qquad$ ; $v_{10} = \\qquad \\qquad$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On considère l'algorithme :\n",
    "\n",
    "<p style=\"text-align:left; background: lightyellow ; border: 1px solid #999; margin: 10px 0 ; padding: 10px ; width:50%;\">\n",
    "$n \\leftarrow 0$   <br>\n",
    "$v \\leftarrow 500$   <br>\n",
    "$e \\leftarrow 1$   <br>\n",
    "Tant que $e > 0.000001$    <br>\n",
    "    $\\qquad v \\leftarrow \\sqrt{v + 2}$   <br>\n",
    "    $\\qquad e \\leftarrow |v -  2 |$   <br>\n",
    "    $\\qquad n \\leftarrow n+1$  <br>\n",
    "</p>\n",
    "\n",
    "\n",
    "Quelle est la valeur de la variable $n$ à la fin ? de $v$ ? de $e$ ? A quoi sert cet algorithme ?  (vous pouvez le traduire en Python ci-dessous pour vérifier)  \n",
    "\n",
    "*Réponse : *\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from math import sqrt\n",
    "# la valeur absolue de x s'obtient par abs(x)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "On considère la suite $(w_n)$ définie par $w_0 = 2$, $w_1 = 3$ et, pour tout entier naturel $n \\geqslant 1$, par  $w_{n+1}= (n+1)w_{n-1} - n^2$.  \n",
    "Ecrire un programme qui calcule la somme $w_0+ w_1 + w_2 + \\dots + w_{50}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  }
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