{"id":185957,"date":"2023-01-03T09:27:10","date_gmt":"2023-01-03T09:27:10","guid":{"rendered":"https:\/\/datascientest.com\/?p=185957"},"modified":"2023-11-09T13:55:02","modified_gmt":"2023-11-09T13:55:02","slug":"suites-et-series-tout-savoir","status":"publish","type":"post","link":"https:\/\/datascientest.com\/suites-et-series-tout-savoir","title":{"rendered":"Suites et S\u00e9ries : comprendre ces deux concepts math\u00e9matiques"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"185957\" class=\"elementor elementor-185957\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fe1d684 e-flex e-con-boxed e-con\" data-id=\"fe1d684\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-63ab7ae elementor-widget elementor-widget-heading\" data-id=\"63ab7ae\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Dans cet article nous allons voir deux concepts cl\u00e9s des math\u00e9matiques : les suites et s\u00e9ries. Il est n\u00e9cessaire d\u2019avoir quelques notions basiques de math\u00e9matiques pour les comprendre enti\u00e8rement. <\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-64d1cbd e-flex e-con-boxed e-con\" data-id=\"64d1cbd\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5d04c28 elementor-widget elementor-widget-text-editor\" data-id=\"5d04c28\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p><span style=\"font-weight: 400;\">Les suites sont largement utilis\u00e9es dans les math\u00e9matiques et peuvent \u00eatre utilis\u00e9es pour <strong>d\u00e9finir des suites d\u2019objets math\u00e9matiques<\/strong> comme des polyn\u00f4mes, des nombres, des ensembles, des fonctions \u2026 Ici, on s\u2019int\u00e9ressera seulement aux suites num\u00e9riques qui sont des suites de nombres r\u00e9els et on montrera le lien qu\u2019il existe entre ces derni\u00e8res et les s\u00e9ries num\u00e9riques. <\/span><\/p><p><span style=\"font-weight: 400;\">Une suite est compos\u00e9e de plusieurs termes et chaque terme poss\u00e8de un rang. Par exemple, la suite 1, 2, 3, 4, 5 est compos\u00e9e de 5 termes (1,2,3,4,5) et leur rang respectif est 0,1,2,3,4 si l\u2019on consid\u00e8re 0 comme \u00e9tant le premier rang de la suite. On utilise \u00e9galement les suites dans le domaine de la Data Science, notamment lorsque l\u2019on travaille avec des <a href=\"https:\/\/datascientest.com\/series-temporelles-python\">s\u00e9ries temporelles<\/a>.\u00a0<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-e912ef2 e-flex e-con-boxed e-con\" data-id=\"e912ef2\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-45279eb elementor-widget elementor-widget-heading\" data-id=\"45279eb\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Comment d\u00e9finir une suite r\u00e9elle ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e0321e6 elementor-widget elementor-widget-text-editor\" data-id=\"e0321e6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Une suite r\u00e9elle peut \u00eatre d\u00e9finie comme une application <span class=\"katex-eq\" data-katex-display=\"false\">n \\longrightarrow u_n<\/span> allant de l&rsquo;ensemble des nombres entiers vers l\u2019ensemble des nombres r\u00e9els et est souvent not\u00e9e <span class=\"katex-eq\" data-katex-display=\"false\">(u_n)_{n \\in \\mathbb{N}}<\/span> . On peut m\u00eame apparenter une suite \u00e0 une fonction qui ne prendrait en argument que des valeurs enti\u00e8res.\u00a0<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Par exemple, <span class=\"katex-eq\" data-katex-display=\"false\">f(n) = n<\/span>, avec un nombre entier, est une suite r\u00e9elle.\u00a0<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Il existe plusieurs types de suite :\u00a0<\/span><\/p><ul><li style=\"list-style-type: none;\"><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">les suites dites explicites qui sont d\u00e9finies par une formule comme dans l\u2019exemple ci-dessus, par exemple : <span class=\"katex-eq\" data-katex-display=\"false\">u_n = cos(n)<\/span> ou <span class=\"katex-eq\" data-katex-display=\"false\">u_n = \\frac{n-1}{n^2+3}<\/span><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">les suites dites r\u00e9currentes dont le terme d\u00e9pend d\u2019un ou plusieurs termes le pr\u00e9c\u00e9dent, par exemple : <span class=\"katex-eq\" data-katex-display=\"false\">u_{n+1} = sin(u_n)<\/span> ou <span class=\"katex-eq\" data-katex-display=\"false\">u_{n+2} = 2u_{n+1} &#8211; u_n<\/span><\/span><\/li><\/ul><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-4a8d9e1 e-flex e-con-boxed e-con\" data-id=\"4a8d9e1\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-0cbb2b4 elementor-widget elementor-widget-heading\" data-id=\"0cbb2b4\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Quelles sont les propri\u00e9t\u00e9s d'une suite ? <\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ad38d55 elementor-widget elementor-widget-text-editor\" data-id=\"ad38d55\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Une suite est constante si tous ses termes sont \u00e9gaux : pour tout n \u2208 N, u<\/span><span style=\"font-weight: 400;\">n <\/span><span style=\"font-weight: 400;\">= u<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">.<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Une suite est stationnaire si, \u00e0 partir d\u2019un certain rang <span class=\"katex-eq\" data-katex-display=\"false\">n_0<\/span>, tous ses termes sont \u00e9gaux : <span class=\"katex-eq\" data-katex-display=\"false\">\\exists n_0 \\in \\mathbb{N}, (n \\geq n_0 \\Rightarrow u_n=u_{n0})<\/span>.<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Une suite est p\u00e9riodique si il existe un entier N positif tel que <span class=\"katex-eq\" data-katex-display=\"false\">\\forall n \\in \\mathbb{N}, u_{n+N} = u_n<\/span>.<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Une suite est croissante (respectivement d\u00e9croissante) si et seulement si <span class=\"katex-eq\" data-katex-display=\"false\">n \\in \\mathbb{N}, u_n \\leq u_{n+1}<\/span> (<\/span> <span style=\"font-weight: 400;\">respectivement <span class=\"katex-eq\" data-katex-display=\"false\">u_{n+1} \\leq u_n<\/span>).<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-67fb3cd e-flex e-con-boxed e-con\" data-id=\"67fb3cd\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b0f2058 elementor-widget elementor-widget-heading\" data-id=\"b0f2058\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Comprendre les suites <\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3c8e1f3 elementor-widget elementor-widget-text-editor\" data-id=\"3c8e1f3\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Une suite num\u00e9rique peut \u00eatre d\u00e9finie comme une somme partielle des termes d\u2019une suite num\u00e9rique. Si on consid\u00e8re la suite <span class=\"katex-eq\" data-katex-display=\"false\">(u_n)_{n \\in \\mathbb{N}}<\/span>, on peut lui associer la s\u00e9rie <span class=\"katex-eq\" data-katex-display=\"false\">S(u)_n<\/span> d\u00e9finie comme <span class=\"katex-eq\" data-katex-display=\"false\">S(u)_n = u_0+u_1+&#8230;+ u_n = \\sum_{k=0}^{n}u_k<\/span><\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Le terme n de la s\u00e9rie associ\u00e9e \u00e0 la suite peut \u00eatre donc vu comme la somme des n+1 premiers termes de la suite.<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Par exemple, si on prend la suite <span class=\"katex-eq\" data-katex-display=\"false\">(u_n) = n<\/span>, la s\u00e9rie associ\u00e9e \u00e0 cette s\u00e9rie est <span class=\"katex-eq\" data-katex-display=\"false\">S(u)_N = \\sum_{k=0}^{N}k = \\frac{N(N+1)}{2}<\/span>.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-0f91845 e-flex e-con-boxed e-con\" data-id=\"0f91845\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-aac97ef elementor-widget elementor-widget-heading\" data-id=\"aac97ef\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Propri\u00e9t\u00e9s des s\u00e9ries<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b8bffdf elementor-widget elementor-widget-text-editor\" data-id=\"b8bffdf\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Il est souvent int\u00e9ressant de voir si une s\u00e9rie num\u00e9rique converge ou diverge. On dit qu\u2019une s\u00e9rie de terme g\u00e9n\u00e9ral <span class=\"katex-eq\" data-katex-display=\"false\">(u_n)<\/span> converge (respectivement diverge) si la suite <span class=\"katex-eq\" data-katex-display=\"false\">(S_N)<\/span> des sommes partielles converge (respectivement diverge). Si la s\u00e9rie converge, la limite <span class=\"katex-eq\" data-katex-display=\"false\">\\lim\\limits_{N \\rightarrow + \\infty} S_N = \\lim\\limits_{N \\rightarrow + \\infty} \\sum_{n = 0}^{N} u_n<\/span> est not\u00e9e <span class=\"katex-eq\" data-katex-display=\"false\">\\sum_{n = 0}^{\\infty} u_n<\/span> et est appel\u00e9e somme de la s\u00e9rie.<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Exemple de s\u00e9rie divergente : la s\u00e9rie associ\u00e9e \u00e0 la suite <span class=\"katex-eq\" data-katex-display=\"false\">(u_n) = n<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">S(u)_N =\u00a0 \\frac{N(N+1)}{2}<\/span> diverge<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Exemple de s\u00e9rie convergente : la s\u00e9rie associ\u00e9e \u00e0 une suite g\u00e9om\u00e9trique de raison q, <span class=\"katex-eq\" data-katex-display=\"false\">S(u)_N =\u00a0 \\frac{1 &#8211; q^{N+1}}{1 &#8211; q}<\/span> converge si et seulement si <span class=\"katex-eq\" data-katex-display=\"false\">|q| &lt; 1<\/span>.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2fc14ad e-flex e-con-boxed e-con\" data-id=\"2fc14ad\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d486e15 elementor-widget elementor-widget-heading\" data-id=\"d486e15\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Quels liens existe-t-il entre les suites et les s\u00e9ries ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fbc9854 elementor-widget elementor-widget-text-editor\" data-id=\"fbc9854\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">On construit tout le temps une s\u00e9rie \u00e0 partir d\u2019une suite et on rappelle qu\u2019une s\u00e9rie et la somme partielles des premiers termes de la suite. On peut donc facilement dire que le comportement de la s\u00e9rie <span class=\"katex-eq\" data-katex-display=\"false\">S(u_N)<\/span> est intimement li\u00e9 \u00e0 celui de la suite <span class=\"katex-eq\" data-katex-display=\"false\">(u_n)<\/span>.<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">A l\u2019inverse, pour \u00e9tudier une suite on peut facilement avoir recours \u00e0 une s\u00e9rie. Par exemple, si on veut \u00e9tudier la monotonie d\u2019une suite <span class=\"katex-eq\" data-katex-display=\"false\">(u_n)<\/span> (v\u00e9rifier la croissance ou la d\u00e9croissance), on peut consid\u00e9rer une suite annexe <span class=\"katex-eq\" data-katex-display=\"false\">(v_n)<\/span> d\u00e9finie par : <span class=\"katex-eq\" data-katex-display=\"false\">v_0 = 0<\/span> et <span class=\"katex-eq\" data-katex-display=\"false\">v_n = u_n &#8211; u_{n-1}<\/span>. On obtient alors <span class=\"katex-eq\" data-katex-display=\"false\">u_n = \\sum_{k=0}^{n} v_k<\/span>. <span class=\"katex-eq\" data-katex-display=\"false\">(u_n)<\/span> est donc la somme partielle d\u2019ordre <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> de la s\u00e9rie de terme <span class=\"katex-eq\" data-katex-display=\"false\">(v_n)<\/span>.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-05c57da e-flex e-con-boxed e-con\" data-id=\"05c57da\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-17b3cd0 elementor-widget elementor-widget-heading\" data-id=\"17b3cd0\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Conclusion<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0a7c184 elementor-widget elementor-widget-text-editor\" data-id=\"0a7c184\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Vous savez maintenant ce que sont les suites et les s\u00e9ries num\u00e9riques et le lien qui existe entre ces deux notions math\u00e9matiques. Vous connaissez aussi quelques propri\u00e9t\u00e9s de ces diff\u00e9rents objets math\u00e9matiques. On peut bien s\u00fbr \u00e9tendre ces notions \u00e0 d\u2019autres types d\u2019objets tels que les <strong>polyn\u00f4mes<\/strong>, les <strong>fonctions<\/strong>, les <strong>ensembles<\/strong>, etc.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0364c1f elementor-widget elementor-widget-text-editor\" data-id=\"0364c1f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Si les s\u00e9ries et les suites vous int\u00e9ressent et si vous voulez en apprendre plus sur les s\u00e9ries temporelles <strong>n\u2019h\u00e9sitez pas \u00e0 rejoindre l&rsquo;une de nos formations en Data Science<\/strong>.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2e68f3c elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"2e68f3c\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formations-data\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9couvrir toutes nos formations<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-97a58ae e-flex e-con-boxed e-con\" data-id=\"97a58ae\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-dc3eb05 elementor-widget elementor-widget-html\" data-id=\"dc3eb05\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"FAQPage\",\r\n  \"mainEntity\": [{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Comment d\u00e9finir une suite ?\u200b\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"Une suite r\u00e9elle peut \u00eatre d\u00e9finie comme une application n\u27f6un allant de l\u2019ensemble des nombres entiers vers l\u2019ensemble des nombres r\u00e9els et est souvent not\u00e9e (un)n\u2208N. On peut m\u00eame apparenter une suite \u00e0 une fonction qui ne prendrait en argument que des valeurs enti\u00e8res.\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Quelles sont les propri\u00e9t\u00e9s d'une suite ? \u200b\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"Une suite est constante si tous ses termes sont \u00e9gaux : pour tout n \u2208 N, un = u0.\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Quels liens existe-t-il entre les suites et les s\u00e9ries ?\u200b\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"On construit tout le temps une s\u00e9rie \u00e0 partir d\u2019une suite et on rappelle qu\u2019une s\u00e9rie et la somme partielles des premiers termes de la suite. On peut donc facilement dire que le comportement de la s\u00e9rie S(uN) est intimement li\u00e9 \u00e0 celui de la suite (uN).\"\r\n    }\r\n  }]\r\n}\r\n<\/script>\r\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Dans cet article nous allons voir deux concepts cl\u00e9s des math\u00e9matiques : les suites et s\u00e9ries. Il est n\u00e9cessaire d\u2019avoir quelques notions basiques de math\u00e9matiques pour les comprendre enti\u00e8rement. Les suites sont largement utilis\u00e9es dans les math\u00e9matiques et peuvent \u00eatre utilis\u00e9es pour d\u00e9finir des suites d\u2019objets math\u00e9matiques comme des polyn\u00f4mes, des nombres, des ensembles, des [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":186670,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2497],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Suites et S\u00e9ries : comprendre ces deux concepts math\u00e9matiques<\/title>\n<meta name=\"description\" content=\"Dans cet article nous allons voir deux concepts cl\u00e9s des math\u00e9matiques : les suites et s\u00e9ries. 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