{"id":159,"date":"2008-04-29T19:38:10","date_gmt":"2008-04-29T17:38:10","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/les-suites-recurrentes-avec-xcas\/"},"modified":"2023-10-14T20:13:59","modified_gmt":"2023-10-14T18:13:59","slug":"les-suites-recurrentes-avec-xcas","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/les-suites-recurrentes-avec-xcas\/","title":{"rendered":"Les suites r\u00e9currentes avec Xcas"},"content":{"rendered":"

\nVoici comment on peut r\u00e9soudre un exercice classique sur les suites.<\/p>\n

Enonc\u00e9<\/h2>\n
\n

Soit la suite $\\left(U_n \\right)_(n \\in \\N)<\/em>$ d\u00e9finie par :<\/p>\n

$$U_0=-1 \\qquad \\textrmet<\/em> \\qquad U_n+1<\/em>=\\dfrac1<\/em>4<\/em> U_n+3.$$<\/p>\n

1) Calculer $U_1$, $U_2$ et $U_3$.<\/p>\n

2) On consid\u00e8re un rep\u00e8re orthonormal. Tracer dans ce rep\u00e8re la droite (D) d’\u00e9quation $y = 0,25x + 3$ et la droite ($\\Delta$) d’\u00e9quation $y = x$, pour les abscisses comprises entre 0 et 5.<\/p>\n

Placer $U_0<\/em>$ sur l’axe des abscisses. Utiliser les droites pr\u00e9c\u00e9dentes pour placer sur l’axe des abscisses les valeurs $U_1<\/em>,~ U_2<\/em>$, $U_3<\/em>$, $U_4$ et $U_5$.<\/p>\n

3) Calculer $S=U_0+U_1+ \\cdots + U_10<\/em>$.<\/p>\n

R\u00e9solution \u00e0 l’aide de Xcas<\/h2>\n
\n

\n\nu(n):=\nsi n==0 alors uo;\nsinon a*u(n-1)+b;\nfsi\n<\/em>\n:;\n<\/code>\n<\/font color><\/p>\n

\/\/ Parsing u\n\/\/ Warning: a b u uo declared as global variable(s) compiling u\nu: recursive definition<\/p>\n

\n\na:=0.25\n<\/code>\n<\/font color><\/p>\n

$$0.25$$<\/p>\n

\n\nb:=3\n<\/code>\n<\/font color><\/p>\n

$$3$$<\/p>\n

\n\nuo:=-1\n<\/code>\n<\/font color><\/p>\n

$$-1$$<\/p>\n

1) Calculer $U_1$, $U_2$ et $U_3$.<\/p>\n

\n\nu(1)\n<\/code>\n<\/font color><\/p>\n

$$2.75$$<\/p>\n

\n\nu(2)\n<\/code>\n<\/font color><\/p>\n

$$3.6875$$<\/p>\n

\n\nu(3)\n<\/code>\n<\/font color><\/p>\n

$$3.921875$$<\/p>\n

2) On consid\u00e8re un rep\u00e8re orthonormal. Tracer dans ce rep\u00e8re la droite (D) d’\u00e9quation $y = 0,25x + 3$ et la droite ($\\Delta$) d’\u00e9quation $y = x$, pour les abscisses comprises entre 0 et 5.<\/p>\n

Placer $U_0<\/em>$ sur l’axe des abscisses. Utiliser les droites pr\u00e9c\u00e9dentes pour placer sur l’axe des abscisses les valeurs $U_1<\/em>,~ U_2<\/em>$, $U_3<\/em>$, $U_4$ et $U_5$.<\/p>\n

\n\ngraphe_suite(a*x+b,uo,5)\n<\/code>\n<\/font color><\/p>\n

\"session.jpg\"<\/p>\n

3) Calculer $S=U_0+U_1+ \\cdots + U_10<\/em>$.<\/p>\n

\n\ns(n):=\nlocal S,j;\nS:=uo;\nsi n==0 alors S;\nsinon \npour j de 1 jusque n pas 1 faire\nS:=S+u(j);\nfpour\nfsi\n<\/em>\n:;\n<\/code>\n<\/font color><\/p>\n

\/\/ Parsing s\n\/\/ Warning: uo u declared as global variable(s) compiling s<\/p>\n

\n\ns(10)\n<\/code>\n<\/font color><\/p>\n

$$37.3333349228$$<\/p>\n

<\/math><\/p>\n","protected":false},"excerpt":{"rendered":"

Voici comment on peut r\u00e9soudre un exercice classique sur les suites. Enonc\u00e9 Soit la suite $\\left(U_n \\right)_(n \\in \\N)$ d\u00e9finie par : $$U_0=-1 \\qquad \\textrmet \\qquad U_n+1=\\dfrac14 U_n+3.$$ 1) Calculer…<\/p>\n","protected":false},"author":1,"featured_media":662,"parent":1637,"menu_order":4,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-159","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"\nLes suites r\u00e9currentes avec Xcas - Maths & Num\u00e9rique<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/les-suites-recurrentes-avec-xcas\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Les suites r\u00e9currentes avec Xcas - Maths & Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Voici comment on peut r\u00e9soudre un exercice classique sur les suites. Enonc\u00e9 Soit la suite $left(U_n right)_(n in N)$ d\u00e9finie par : $$U_0=-1 qquad textrmet qquad U_n+1=dfrac14 U_n+3.$$ 1) Calculer…\" \/>\n<meta property=\"og:url\" content=\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/les-suites-recurrentes-avec-xcas\/\" \/>\n<meta property=\"og:site_name\" content=\"Maths & Num\u00e9rique\" \/>\n<meta property=\"article:modified_time\" content=\"2023-10-14T18:13:59+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/wordpress.callac.online\/wp-content\/uploads\/2008\/04\/jpg_session.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"599\" \/>\n\t<meta property=\"og:image:height\" content=\"239\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/les-suites-recurrentes-avec-xcas\/\",\"url\":\"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/xcas\/les-suites-recurrentes-avec-xcas\/\",\"name\":\"Les suites r\u00e9currentes avec Xcas - 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