{"id":177284,"date":"2024-01-21T12:45:17","date_gmt":"2024-01-21T11:45:17","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=177284"},"modified":"2024-01-21T12:47:12","modified_gmt":"2024-01-21T11:47:12","slug":"sequences-and-series-understanding-these-two-mathematical-concepts","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts","title":{"rendered":"Sequences and series: understanding these two mathematical concepts"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"177284\" class=\"elementor elementor-177284\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b25e3f2 e-flex e-con-boxed e-con\" data-id=\"b25e3f2\" 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-92f51bb elementor-widget elementor-widget-heading\" data-id=\"92f51bb\" 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\">In this article, we take a look at two key mathematical concepts: sequences and series. You need some basic mathematical knowledge to understand them fully. <\/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-61e7709 e-flex e-con-boxed e-con\" data-id=\"61e7709\" 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-4d19664 elementor-widget elementor-widget-text-editor\" data-id=\"4d19664\" 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><strong>Sequences are widely used in mathematics<\/strong>, and can be used to define sequences of mathematical objects such as polynomials, numbers, sets, functions, etc. Here, we&#8217;re only interested in numerical sequences, which are sequences of real numbers, and we&#8217;ll show the link between them and numerical series.<\/p><p>A sequence is made up of several terms, and each term has a rank. For example, the sequence 1, 2, 3, 4, 5 is made up of 5 terms (1,2,3,4,5) and their respective ranks are 0,1,2,3,4 if we consider 0 to be the first rank of the sequence. Sequences are also used in <a href=\"https:\/\/datascientest.com\/en\/data-science-bootcamp-definition-training-benefits\">data science<\/a>, particularly when working with time series.<\/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-3477b54 e-flex e-con-boxed e-con\" data-id=\"3477b54\" 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-5467df3 elementor-widget elementor-widget-heading\" data-id=\"5467df3\" 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\">How do you define a real sequence?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c7ce2e6 elementor-widget elementor-widget-text-editor\" data-id=\"c7ce2e6\" 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;\">A real sequence can be defined as an application <span class=\"katex-eq\" data-katex-display=\"false\">n \\longrightarrow u_n<\/span> from the set of integers to the set of real numbers and is often noted as <span class=\"katex-eq\" data-katex-display=\"false\">(u_n)_{n \\in \\mathbb{N}}<\/span> . A sequence can even be likened to a function that takes only integer values as arguments. <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">For example, <span class=\"katex-eq\" data-katex-display=\"false\">f(n) = n<\/span>, given an integer, is a real sequence. <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">There are several types of sequences:<\/span><\/p>\n\n<ul>\n \t<li style=\"list-style-type: none;\">\n<ul>\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">so-called explicit sequences which are defined by a formula as in the example above, for example: <span class=\"katex-eq\" data-katex-display=\"false\">u_n = cos(n)<\/span> or <span class=\"katex-eq\" data-katex-display=\"false\">u_n = \\frac{n-1}{n^2+3}<\/span><\/span><\/li>\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">so-called recurring sequences whose term depends on one or more terms preceding it, for example: <span class=\"katex-eq\" data-katex-display=\"false\">u_{n+1} = sin(u_n)<\/span> or <span class=\"katex-eq\" data-katex-display=\"false\">u_{n+2} = 2u_{n+1} &#8211; u_n<\/span><\/span><\/li>\n<\/ul>\n<\/li>\n<\/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-4c4391a e-flex e-con-boxed e-con\" data-id=\"4c4391a\" 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-30f0632 elementor-widget elementor-widget-heading\" data-id=\"30f0632\" 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\">What are the properties of a sequence? <\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-affd2a1 elementor-widget elementor-widget-text-editor\" data-id=\"affd2a1\" 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;\">A sequence is constant if all its terms are equal: for any 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>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">A sequence is stationary if, from a certain rank <span class=\"katex-eq\" data-katex-display=\"false\">n_0<\/span>, all its terms are equal: <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>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">A sequence is periodic if there exists a positive integer N such that <span class=\"katex-eq\" data-katex-display=\"false\">\\forall n \\in \\mathbb{N}, u_{n+N} = u_n<\/span>.<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">A sequence is increasing (respectively decreasing) if and only if <span class=\"katex-eq\" data-katex-display=\"false\">n \\in \\mathb{N}, u_n \\leq u_{n+1}<\/span> (<\/span> <span style=\"font-weight: 400;\">respectively <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-7fd9f24 e-flex e-con-boxed e-con\" data-id=\"7fd9f24\" 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-47f07b4 elementor-widget elementor-widget-heading\" data-id=\"47f07b4\" 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\">Sequences and Series - Understanding suites <\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1fade9d elementor-widget elementor-widget-text-editor\" data-id=\"1fade9d\" 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;\">A numerical sequence can be defined as a partial sum of the terms of a numerical sequence. If we consider the sequence <span class=\"katex-eq\" data-katex-display=\"false\">(u_n)_{n \\in \\mathbb{N}}<\/span>, we can associate with it the series <span class=\"katex-eq\" data-katex-display=\"false\">S(u)_n<\/span> defined as <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>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">The term n of the series associated with the sequence can therefore be seen as the sum of the first n+1 terms of the sequence.<\/span><\/p>\n<p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">For example, if we take the sequence <span class=\"katex-eq\" data-katex-display=\"false\">(u_n) = n<\/span>, the series associated with this sequence is <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-8087a08 e-flex e-con-boxed e-con\" data-id=\"8087a08\" 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-eb089e6 elementor-widget elementor-widget-heading\" data-id=\"eb089e6\" 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\">What are the links between sequences and series?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2dfd987 elementor-widget elementor-widget-text-editor\" data-id=\"2dfd987\" 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;\">We&#8217;re always building a series from a sequence, and remember that a series is the partial sum of the first terms of the sequence. We can therefore easily say that the behavior of the series <span class=\"katex-eq\" data-katex-display=\"false\">S(u_N)<\/span> is intimately linked to that of the sequence <span class=\"katex-eq\" data-katex-display=\"false\">(u_n)<\/span>.<\/span><\/p><p style=\"padding-left: 40px;\"><span style=\"font-weight: 400;\">Inversely, to study a sequence we can easily resort to a series. For example, if we want to study the monotonicity of a sequence <span class=\"katex-eq\" data-katex-display=\"false\">(u_n)<\/span> (check for growth or decay), we can consider an auxiliary sequence <span class=\"katex-eq\" data-katex-display=\"false\">(v_n)<\/span> defined by : <span class=\"katex-eq\" data-katex-display=\"false\">v_0 = 0<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">v_n = u_n &#8211; u_{n-1}<\/span>. We then obtain <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> is therefore the partial sum of order <span class=\"katex-eq\" data-katex-display=\"false\">n<\/span> of the series of term <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-94447dc e-flex e-con-boxed e-con\" data-id=\"94447dc\" 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-9b4d7a3 elementor-widget elementor-widget-heading\" data-id=\"9b4d7a3\" 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\">Sequences and Series - Conclusion<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-156e486 elementor-widget elementor-widget-text-editor\" data-id=\"156e486\" 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>You now know what <strong>numerical sequences<\/strong> and series are, and how these two mathematical concepts are related. You also know some of the properties of these different mathematical objects. We can, of course, extend these notions to other types of object, such as polynomials, functions, sets, etc.<\/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-607e71d elementor-widget elementor-widget-text-editor\" data-id=\"607e71d\" 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>If you&#8217;re interested in series and sequences and want to learn more about time series, don&#8217;t hesitate to join one of our <a href=\"https:\/\/datascientest.com\/en\/synergies-unveiled-the-dynamic-intersection-of-data-science-and-finance\">Data Science training courses.<\/a><\/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-10894ec elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"10894ec\" 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\/en\/data-courses\">\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\">Discover all our training courses<\/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-2f951ff e-flex e-con-boxed e-con\" data-id=\"2f951ff\" 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-7f4d59f elementor-widget elementor-widget-html\" data-id=\"7f4d59f\" 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>In this article, we take a look at two key mathematical concepts: sequences and series. You need some basic mathematical knowledge to understand them fully. Sequences are widely used in mathematics, and can be used to define sequences of mathematical objects such as polynomials, numbers, sets, functions, etc. Here, we&#8217;re only interested in numerical sequences, [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":177285,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"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>Sequences and series: understanding these two mathematical concepts<\/title>\n<meta name=\"description\" content=\"Delve into the world of mathematical sequences and series. Gain a clear understanding of these fundamental concepts, exploring the definitions, properties, and practical applications. Whether unraveling the patterns in sequences or exploring the sum of series, this comprehensive guide provides insights into the essential building blocks of mathematical analysi\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Sequences and series: understanding these two mathematical concepts\" \/>\n<meta property=\"og:description\" content=\"In this article, we take a look at two key mathematical concepts: sequences and series. You need some basic mathematical knowledge to understand them\" \/>\n<meta property=\"og:url\" content=\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts\" \/>\n<meta property=\"og:site_name\" content=\"Data Science Courses | DataScientest\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/DataScientestEN\" \/>\n<meta property=\"article:published_time\" content=\"2024-01-21T11:45:17+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-01-21T11:47:12+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/datascientest.com\/en\/files\/2024\/01\/Illu_BLOG__suites_series.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"563\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Melanie\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@DataScientest__\" \/>\n<meta name=\"twitter:site\" content=\"@DataScientest__\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Melanie\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts#article\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts\"},\"author\":{\"name\":\"Melanie\",\"@id\":\"https:\/\/datascientest.com\/en\/#\/schema\/person\/19d5f7ade9407eb69af3bf6d1ae1731d\"},\"headline\":\"Sequences and series: understanding these two mathematical concepts\",\"datePublished\":\"2024-01-21T11:45:17+00:00\",\"dateModified\":\"2024-01-21T11:47:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts\"},\"wordCount\":740,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/datascientest.com\/en\/#organization\"},\"articleSection\":[\"Data Science\"],\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts#respond\"]}],\"copyrightYear\":\"2024\",\"copyrightHolder\":{\"@id\":\"https:\/\/datascientest.com\/#organization\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts\",\"url\":\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts\",\"name\":\"Sequences and series: understanding these two mathematical concepts\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/en\/#website\"},\"datePublished\":\"2024-01-21T11:45:17+00:00\",\"dateModified\":\"2024-01-21T11:47:12+00:00\",\"description\":\"Delve into the world of mathematical sequences and series. Gain a clear understanding of these fundamental concepts, exploring the definitions, properties, and practical applications. Whether unraveling the patterns in sequences or exploring the sum of series, this comprehensive guide provides insights into the essential building blocks of mathematical analysi\",\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts\"]}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/datascientest.com\/en\/#website\",\"url\":\"https:\/\/datascientest.com\/en\/\",\"name\":\"Data Science Courses | DataScientest\",\"description\":\"Leader in Data Science Courses\",\"publisher\":{\"@id\":\"https:\/\/datascientest.com\/en\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/datascientest.com\/en\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-GB\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/datascientest.com\/en\/#organization\",\"name\":\"DataScientest\",\"url\":\"https:\/\/datascientest.com\/en\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\/\/datascientest.com\/en\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/datascientest.com\/en\/wp-content\/blogs.dir\/9\/files\/2024\/02\/DataScientest_icon_blue-2.png\",\"contentUrl\":\"https:\/\/datascientest.com\/en\/wp-content\/blogs.dir\/9\/files\/2024\/02\/DataScientest_icon_blue-2.png\",\"width\":301,\"height\":301,\"caption\":\"DataScientest\"},\"image\":{\"@id\":\"https:\/\/datascientest.com\/en\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/DataScientestEN\",\"https:\/\/twitter.com\/DataScientest__\",\"https:\/\/www.linkedin.com\/school\/datascientest\/mycompany\/\",\"https:\/\/www.tiktok.com\/@datascientest\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/datascientest.com\/en\/#\/schema\/person\/19d5f7ade9407eb69af3bf6d1ae1731d\",\"name\":\"Melanie\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\/\/datascientest.com\/en\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8d3d660a0698de06f13ecf4823519da1?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8d3d660a0698de06f13ecf4823519da1?s=96&d=mm&r=g\",\"caption\":\"Melanie\"},\"url\":\"https:\/\/datascientest.com\/en\/author\/melaniekrause\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Sequences and series: understanding these two mathematical concepts","description":"Delve into the world of mathematical sequences and series. Gain a clear understanding of these fundamental concepts, exploring the definitions, properties, and practical applications. Whether unraveling the patterns in sequences or exploring the sum of series, this comprehensive guide provides insights into the essential building blocks of mathematical analysi","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts","og_locale":"en_GB","og_type":"article","og_title":"Sequences and series: understanding these two mathematical concepts","og_description":"In this article, we take a look at two key mathematical concepts: sequences and series. You need some basic mathematical knowledge to understand them","og_url":"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts","og_site_name":"Data Science Courses | DataScientest","article_publisher":"https:\/\/www.facebook.com\/DataScientestEN","article_published_time":"2024-01-21T11:45:17+00:00","article_modified_time":"2024-01-21T11:47:12+00:00","og_image":[{"width":1024,"height":563,"url":"https:\/\/datascientest.com\/en\/files\/2024\/01\/Illu_BLOG__suites_series.png","type":"image\/png"}],"author":"Melanie","twitter_card":"summary_large_image","twitter_creator":"@DataScientest__","twitter_site":"@DataScientest__","twitter_misc":{"Written by":"Melanie","Estimated reading time":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts#article","isPartOf":{"@id":"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts"},"author":{"name":"Melanie","@id":"https:\/\/datascientest.com\/en\/#\/schema\/person\/19d5f7ade9407eb69af3bf6d1ae1731d"},"headline":"Sequences and series: understanding these two mathematical concepts","datePublished":"2024-01-21T11:45:17+00:00","dateModified":"2024-01-21T11:47:12+00:00","mainEntityOfPage":{"@id":"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts"},"wordCount":740,"commentCount":0,"publisher":{"@id":"https:\/\/datascientest.com\/en\/#organization"},"articleSection":["Data Science"],"inLanguage":"en-GB","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts#respond"]}],"copyrightYear":"2024","copyrightHolder":{"@id":"https:\/\/datascientest.com\/#organization"}},{"@type":"WebPage","@id":"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts","url":"https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts","name":"Sequences and series: understanding these two mathematical concepts","isPartOf":{"@id":"https:\/\/datascientest.com\/en\/#website"},"datePublished":"2024-01-21T11:45:17+00:00","dateModified":"2024-01-21T11:47:12+00:00","description":"Delve into the world of mathematical sequences and series. Gain a clear understanding of these fundamental concepts, exploring the definitions, properties, and practical applications. Whether unraveling the patterns in sequences or exploring the sum of series, this comprehensive guide provides insights into the essential building blocks of mathematical analysi","inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/datascientest.com\/en\/sequences-and-series-understanding-these-two-mathematical-concepts"]}]},{"@type":"WebSite","@id":"https:\/\/datascientest.com\/en\/#website","url":"https:\/\/datascientest.com\/en\/","name":"Data Science Courses | DataScientest","description":"Leader in Data Science Courses","publisher":{"@id":"https:\/\/datascientest.com\/en\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/datascientest.com\/en\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-GB"},{"@type":"Organization","@id":"https:\/\/datascientest.com\/en\/#organization","name":"DataScientest","url":"https:\/\/datascientest.com\/en\/","logo":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/datascientest.com\/en\/#\/schema\/logo\/image\/","url":"https:\/\/datascientest.com\/en\/wp-content\/blogs.dir\/9\/files\/2024\/02\/DataScientest_icon_blue-2.png","contentUrl":"https:\/\/datascientest.com\/en\/wp-content\/blogs.dir\/9\/files\/2024\/02\/DataScientest_icon_blue-2.png","width":301,"height":301,"caption":"DataScientest"},"image":{"@id":"https:\/\/datascientest.com\/en\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/DataScientestEN","https:\/\/twitter.com\/DataScientest__","https:\/\/www.linkedin.com\/school\/datascientest\/mycompany\/","https:\/\/www.tiktok.com\/@datascientest"]},{"@type":"Person","@id":"https:\/\/datascientest.com\/en\/#\/schema\/person\/19d5f7ade9407eb69af3bf6d1ae1731d","name":"Melanie","image":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/datascientest.com\/en\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8d3d660a0698de06f13ecf4823519da1?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8d3d660a0698de06f13ecf4823519da1?s=96&d=mm&r=g","caption":"Melanie"},"url":"https:\/\/datascientest.com\/en\/author\/melaniekrause"}]}},"_links":{"self":[{"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/posts\/177284"}],"collection":[{"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/users\/67"}],"replies":[{"embeddable":true,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/comments?post=177284"}],"version-history":[{"count":0,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/posts\/177284\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/media\/177285"}],"wp:attachment":[{"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/media?parent=177284"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/categories?post=177284"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/datascientest.com\/en\/wp-json\/wp\/v2\/tags?post=177284"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}