2020-2021/TST/04_Formalisation_des_suites/5E_boucles.ipynb

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   "source": [
    "# Suite et répétition\n",
    "\n",
    "Dans tout ce TP, il est demandé de ne **jamais** utiliser la formule explicite pour répondre aux consignes.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculer des termes d'une suite\n",
    "\n",
    "Ci-dessous, un programme python qui permet de calculer des termes d'une suite. \n",
    "\n",
    "Reconnaître la nature et les paramètres de cette suite. *Vous pouvez modifier le programme pour afficher les résultats des calculs*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "u = 2\n",
    "u = u - 1.5\n",
    "u = u - 1.5\n",
    "u = u - 1.5\n",
    "u = u - 1.5\n",
    "u = u - 1.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Même question pour la suite suivante"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = 5\n",
    "t = 2*t\n",
    "t = 2*t\n",
    "t = 2*t\n",
    "t = 2*t\n",
    "t = 2*t\n",
    "t = 2*t"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour les suites suivantes écrire une programme python qui permet de calculer et afficher les valeurs de $u_1$, $u_5$ et $u_{10}$.\n",
    "\n",
    "1. $(u_n)$ est géométrique de raison 1.2 et de premier terme $u_0 = 23$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. $(u_n)$ est arithmétique de raison -2 et de premier terme $u_0 = 7$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
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   "source": [
    "3. (\\*) $(u_u)$ a pour premier terme $u_0 = 3$ et pour formule de récurence $u_{n+1} = 2u_n - 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
   "source": []
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Éviter les répétitions: boucle for\n",
    "\n",
    "Dans les programmes précédents, beaucoup de lignes se répètent. Imaginez que l'on demander $u_{1000}$, cette méthode de programmation ne serait pas satisfaisant.\n",
    "\n",
    "- Le programme suivant calcule les termes d'une suite et affiche le terme 5. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.1020201002\n"
     ]
    }
   ],
   "source": [
    "u = 2\n",
    "for i in range(5):\n",
    "    u = u *1.01\n",
    "print(u)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Quelle est la nature de la suite? Quels sont les paramètres?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Copier puis modifier le programme pour calculer $u_{10}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Idem pour calculer la valeur de $u_{1000}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Écrire un programme qui calcule $u_{500}$ quand $(u_n)$ est une suite géométrique de raison 0.99 et de premier terme 10 000."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- (\\*) $(u_u)$ a pour premier terme $u_0 = 700$ et pour formule de récurence $u_{n+1} = 0.7u_n - 400$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Détecter des seuils: boucle while\n",
    "\n",
    "Ci-dessous, un programme qui répète plusieurs actions **jusqu'à** ce que quelque chose arrive.\n",
    "\n",
    "Expliquer ce que fait chaque ligne."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u( 0 ) =  5\n",
      "u( 1 ) =  7\n",
      "u( 2 ) =  9\n",
      "u( 3 ) =  11\n",
      "u( 4 ) =  13\n",
      "u( 5 ) =  15\n",
      "u( 6 ) =  17\n",
      "u( 7 ) =  19\n",
      "u( 8 ) =  21\n",
      "u( 9 ) =  23\n",
      "u( 10 ) =  25\n",
      "u( 11 ) =  27\n",
      "u( 12 ) =  29\n",
      "u( 13 ) =  31\n",
      "u( 14 ) =  33\n",
      "u( 15 ) =  35\n",
      "u( 16 ) =  37\n",
      "u( 17 ) =  39\n",
      "u( 18 ) =  41\n",
      "Ah! u(n) est plus grand que 40 après avoir répété 18 fois le calcul.\n"
     ]
    }
   ],
   "source": [
    "u = 5\n",
    "n = 0\n",
    "print(\"u(\", n, \") = \", u)\n",
    "\n",
    "while u < 40:\n",
    "    u = u + 2\n",
    "    n = n + 1\n",
    "    print(\"u(\", n, \") = \", u)\n",
    "\n",
    "print(\"Ah! u(n) est plus grand que 40 après avoir répété\", n, \"fois le calcul.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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