{"id":4486,"date":"2021-08-03T10:12:20","date_gmt":"2021-08-03T04:42:20","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=4486"},"modified":"2025-12-07T22:20:24","modified_gmt":"2025-12-07T16:50:24","slug":"what-is-the-convergence-of-sequence-and-series","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/","title":{"rendered":"What is the convergence of sequence and series?"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Overview (sequence and series)<\/h2>\n\n\n\n<p>A function f : N&nbsp; , where S is a non-empty set , is called <a href=\"https:\/\/www.mathsisfun.com\/algebra\/sequences-series.html\" target=\"_blank\" rel=\"noreferrer noopener\">sequence<\/a> , for each n\u03f5N.<\/p>\n\n\n\n<p>We write sequence as f(1) , f(2) , f(3) , f(4)\u2026\u2026\u2026.f(n).<\/p>\n\n\n\n<p>Any sequence f(n) can be denoted as &lt;f(n)&gt; or {f(n)} or (f(n)).<\/p>\n\n\n\n<p>Suppose f(n) = sn<\/p>\n\n\n\n<p>Then it can be written as &#8211;&nbsp; <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/6lk_XCO9EPu58kmHtGhTRhp5rVbtuxz6w0WjkcyrWMJq7hLrLIyK-8ZUzk7osmcvGP0_Vzl2lM7O6e6lzzCKz2XGBjWSo00uW3lukp2UxOhut4u4k0xZ51dZxqsADPXCZER-Z9vd\" width=\"160\" height=\"22\">&nbsp; and can be denoted as &lt;sn &gt;or&nbsp; {sn } or ( sn)<\/p>\n\n\n\n<p>sn is the n\u2019th term of the sequence.<\/p>\n\n\n\n<p>Example:&nbsp; suppose we have a sequence \u2013 1 , 4 , 9 , 16 ,\u2026\u2026\u2026.. and its n\u2019th term is n2.<\/p>\n\n\n<p>The sequence, we can write as&nbsp; &lt;n2 &gt;<\/p>\n\n\n<h2 class=\"wp-block-heading\"><strong>Types of sequences <\/strong><\/h2>\n\n\n\n<p><strong>1. Finite sequence- <\/strong>A sequence which has finite number of terms is finite sequence.<\/p>\n\n\n\n<p><strong>2. Infinite sequence- <\/strong>&nbsp;A sequence which is not finite , called infinite sequence.<\/p>\n\n\n\n<p><strong>Limit of a Sequence<\/strong>&#8211; A sequence &lt;sn&gt; is said to tend to limit \u201cl\u201d , when given any positive number \u2018\u03f5\u2019 , however small , we can always find a integer \u2018m\u2019 such that |sn \u2013 l| &lt;\u03f5 , for every for all, n\u2265m , and we can define this as follows,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/TouZ9fM-6fXAc4AtDYzBnEl47vMWdk2WV1n1OdtldevTi-MP_iUX9s7sHgfBau9OZ64BxPgF89eje7Kj2EjPQMw0czYRwyMHweLqhw17V41YcF_5j7ygHby-ikAp5SAmI0Pitei9\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Example: If&nbsp; <\/strong><strong><\/strong><strong>&nbsp; , then the limit of&nbsp; will be-<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/2X9Ab-uZj7YGe2pwvRWPgKm5amyzZNeDrlS-b6R-nGwkl5t_BgMtjc3UkHBZUYDQ4S4bnb1yT0q81dXz6BzA6gmg_tctNkYMdK1VqMTlgy7dUpBcfjpv9fUXdp4dJlOsBRqz5diJ\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Hence the limit of the sequence is 1\/2.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Some important limits to remember<\/strong> for sequence and series<\/h2>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/jaurDPUawFn6n3Qoql2UPALOtW-rOOfhOfyQ2qExI89YDnOVxjrP0wE_KsyRCnETKIp25RQcWwclK0aX_srKuovsNf2hsD5ed-VKjX2xA6H-j5ab0JpAWhcfAd4sz7H88oaRLdOz\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Convergent sequence- A sequence Sn is convergent when it tends to a finite limit. That means the limit of a sequence Sn will be always finite in case of <a href=\"https:\/\/mathworld.wolfram.com\/ConvergentSequence.html\" target=\"_blank\" rel=\"noreferrer noopener\">convergent sequence<\/a>.<\/p>\n\n\n\n<p>Divergent sequence- when a sequence tends to \u00b1\u221e then it is <a href=\"https:\/\/undergroundmathematics.org\/glossary\/divergent-sequence\" target=\"_blank\" rel=\"noreferrer noopener\">divergent sequence<\/a>.<\/p>\n\n\n\n<p>Oscillatory sequence-&nbsp; when a sequence neither converges nor diverges then it is an oscillatory sequence.<\/p>\n\n\n\n<p>Note- a sequence which neither converges nor diverges , is called oscillatory sequence.<\/p>\n\n\n\n<p>A sequence is null, when it converges to zero.<\/p>\n\n\n\n<p><strong>Example-1:&nbsp; consider a sequence 2, 3\/2 , 4\/3 , 5\/4, \u2026\u2026.. here Sn =&nbsp; 1 + 1\/n<\/strong><\/p>\n\n\n\n<p>Sol. As we can see that the sequence Sn is convergent and has limit 1.<\/p>\n\n\n\n<p>According to def.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/Uzg87iTdQqzj9S_Sq6-qK16nzBJaQZyE5bDGmexG12gdfOSe_MWPtfR8JOMUnU4Q-_NTlK_8-KYRtJBL7YExNmadd8HcNJyr7QdpxBoE8XoQ9EhMa2P2jKsrjEBBBHpcN96LhtyL\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Example-2: consider a sequence Sn=&nbsp; n<\/strong><strong>\u00b2<\/strong><strong> + (-1)<\/strong><strong>\u207f<\/strong><strong>.<\/strong><\/p>\n\n\n\n<p>Sol. Here we can see that, the sequence Sn is divergent&nbsp; as it has infinite limit.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/GaDCkA1rxwv55ol89IHDDXWn5-3Jss7sg0xeDbwaGbBxEU4Nz7hz14F2mZ6vp-C-grrvHuhTsfS64a8GNA-zs4cBEG6XkBM_OY1IGBFrJOJROs6xQrFHCaukqvj-pO-dd4cARBPW\" alt=\"\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Series<\/strong><\/h2>\n\n\n\n<p><strong>Infinite series- <\/strong>If &nbsp; is a sequence , then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/TYdEKftZAlaEeKp7-smypknaW94hppmiaWVkYHMRW1PGumvVN7hWnAsaluzYbVExw9DYAYG5hzLtkaDPcoaDZ7RNm0yT420UaIZoXRf4uouw6OKbqo49acULf0SRWa7-BKpFZBbU\" width=\"178\" height=\"25\"> is called the infinite series.<\/p>\n\n\n\n<p>We denote this by<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/pktJxZtAmNTY_N4C4uS8oIsmlrSC41DgkCZB4JtUZ1_BLMHCiD4SZmiHKPIHG2q41-J1hi-tNfbO7FPMerFcOSr9tTflSFQ7k5yyMOLJhbeP1bbAdMkBoiy1xj_peMsatg9IL1pR\" alt=\"\"\/><\/figure>\n\n\n\n<p>Examples of infinite series-<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/OTtaRz9Nr0SgBOunEi7eS6nFmAVcNuJgrR8f1ztVdsGFjXb24bU9e86GTxbRdkLQmW_53fB_AaeqOSMU-V0Af_GBi7oPKzE1daMUvbG-u18B5CE1syIz-S12kcemNOtD9suU7Ftw\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Covergent series &#8211; <\/strong>&nbsp;suppose n\u2192\u221e , Sn\u2192 a finite limit&nbsp; \u2018s\u2019&nbsp; , then the series Sn is said to be convergent .<\/p>\n\n\n\n<p>We can denote it as,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/asLnsT_ZSQOw-zyHcVLTW-q2y7xltLCu1xBqfaYlK1BgBSSnPoaiox1DifxliMx8P29oGZ3r7s26FJ4XnJpfGSztlJo3C-FxqLyC1oaqxTVzEB7Ea1Y_tsaR3A2NjFpXw5fppZwB\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Divergent series<\/strong>&#8211;&nbsp; when Sn tends to infinity then the series is said to be divergent.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/XJ5-Y0OHKukI4Y_bEgF9R_WOWBVROmPYUDiIgqPa-8ybB8nucL7HyGnj-RgLojKReqdwQknMnsNxyhgyod9HCQc5bv43owKYN1-wfMzl4HsyKGcy7Y-B-a9-4BCUVpqdFBqYPzWY\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Oscillatory series- <\/strong>&nbsp;when Sn does not tends to a unique limit (finite or infinite) , then it is called Oscillatory series.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Properties of infinite series <\/h2>\n\n\n\n<p>1. the convergence and divergence of an infinite series is unchanged addition od deletion of a finite number of terms from it.<\/p>\n\n\n\n<p>2. if positive terms of convergent series change their sign , then the series will be convergent.<\/p>\n\n\n\n<p>3. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/KbJZEPgg4j8YD966t019YMr0INB-ene6VX-RAAK3Rknu9rs4r6Fm0xjKHqw6KDy2W9XPeWVhxTlU7e7BSwlYSg_AP8OIPwneuiG923_kbNuhGyQU5XcriMo3DSOBOoOM3mNjKre3\" width=\"62\" height=\"29\">converges to s , let k be a non-zero fixed number&nbsp; then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/UmkCGG8kbcYu-7-LTACYh2p3fgnaroFwrS4snpRPT0UsCvUJii4r50_rj_HaHzEki2rnS2gWU0KgRKyOZDJOu0oxJ5hK_HSJcfS_ZA-sDakqsDixt3H0QTD3D3jHzOJFnUA01nTX\" width=\"67\" height=\"26\">converges to ks.<\/p>\n\n\n\n<p>4. Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/KbJZEPgg4j8YD966t019YMr0INB-ene6VX-RAAK3Rknu9rs4r6Fm0xjKHqw6KDy2W9XPeWVhxTlU7e7BSwlYSg_AP8OIPwneuiG923_kbNuhGyQU5XcriMo3DSOBOoOM3mNjKre3\" width=\"62\" height=\"29\">&nbsp; converges to \u2018l\u2019 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/GY7EeGVHyTF9a_xdeHmiO2R5RYgH508Qvqt4iGRwS0WoSPKhXWssUAFBYv7d0CxKkpE1u1r7aurhCPImE6-OqLdty28YspPUi9ck38MQtoxIpf8s-1EvqlI5wxPyWDRdI3kTSkXY\" width=\"54\" height=\"25\"> converges to \u2018m\u2019.<\/p>\n\n\n\n<p><strong>Example-1: check whether the series <\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/abyIV53Tbly71Qo5nXjD4bpM9RGsLH4isSQ2okwZTilnqOIz7b97FW-UlHx2xJ1_h6aYV0r1e_jXAKyNW1s4VJOY8fLRABI9aAT6RfkKYE_-Q7zSu4O0b1LC9bW8DcuPk2KZclVE\" width=\"51\" height=\"23\"><\/strong><\/p>\n\n\n\n<p><strong> is convergent or divergent. Find its value in case of convergent.<\/strong><\/p>\n\n\n\n<p>Sol.&nbsp; As we know that,<\/p>\n\n\n\n<p class=\"has-text-align-center\">Sn = <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/ew8h4IbISdk3nPwY3XyGqB0Khgd3ZDguJwQJavgKWIVXOVp3pmUfAPIRpAcpaW8IwPf8gr_bnIQVxBMlDoVsRyzuVaD7vybkf2NFjDRcfQdRG6J3gY1jbNEokVIiz6HTdbNNmq6H\" width=\"47\" height=\"32\"><\/p>\n\n\n\n<p>Therefore,<\/p>\n\n\n\n<p class=\"has-text-align-center\">Sn = <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/QD1U8tjCy99f-FgAbtJ3fv2rN7pHBijMdVhH3LzW9YzshGd66bB8Cdxlw1Dx61nV3GQBrD8biQ2h6b5NPQfwi6ePCrusmVOg48zlFNqvV497hcb_GfVi3arjzf_B9LYUTBKXqKW9\" width=\"104\" height=\"37\"><\/p>\n\n\n\n<p>Now find out the limit of the sequence,<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/8s6xilYGzcEG15PCe0SjBTBk1l78feYNPYVunRJoNgrxkFXg1nhI7R1Osm6A4ZrSeKukEg3VhO61WQxMs9gF_4pyNQiePXHhXMI8Yc9qvtZFeqFdZVKeomk5erPhv3Y_efaVl59v\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Here the value of the limit is infinity, so that the series is divergent as sequence diverges<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Example-2: check whether the series <\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/SCJ-nIA5srSlj-Ic-9yr6Z1Dk8FdWw4uHPRtf2vUf9X5-Hj9razONmzYoXktyOPHRCd8iqCVO5ozukd5CbwCOCzpq1qScF4DTVjKN-AIwlAnJXxcnZTZP013BlZCW4_nDY_qJBEs\" width=\"70\" height=\"33\"><\/strong><\/p>\n\n\n\n<p><strong>&nbsp; is convergent or divergent. Find its value in case of convergent.<\/strong><\/p>\n\n\n\n<p>Sol. The general formula for this series is,<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/PwY2yPx6bkhjkme0lR6Urd6uYPpFjLE9zi_9kH0kBF16trwLto-gxtMrBPApkQIytY7bDhDDMoGu_ZuvtGXq-USbKBAzUGuZULpGUggbCaUmYbCP7jE8n7P3hhdSFHyJQaPj2nXg\" alt=\"\"\/><\/figure><\/div>\n\n\n<p><strong>We get<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/3YTuZ-3qsTewe7XDMhe7OWwiEeTJbJkKPpKnhht9icwn_0HATVLQWDZUZiB2fnHaJd4q6LtWfrfr5YzV_x_JXQZ69X5zqQstgtd47Ch9WnSfsQHILztkipK6P7kx9ZbBmjgqMeUZ\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Hence the series is convergent and its values is 3\/2.<\/p>\n\n\n\n<p><strong>Example: Test the convergence of the series- <\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/fyAHuY1xVc5mxLsz8nOW02gnTiYpFa1jn2oYNz1kBYxWe0ICJV1BSfukki4buU3mIcm-MTnqQxb0aZGQo-uDFZ3oo-TLtDI4VVQUs4XdAd2LO2rm1hbXnl6sZM1Qbj5JgxFQb9Lf\" width=\"142\" height=\"37\"><\/strong><\/p>\n\n\n\n<p>Sol. Here we can see that the given series is in geometric progression<\/p>\n\n\n\n<p>As its first term is 1 and common ratio is \u00bd.<\/p><a href=\"https:\/\/ibetslot.one\/\" style=\"color: #ffffff; text-decoration: none;\">https:\/\/ibetslot.one\/<a>\n\n\n\n<p>Then we know that the sum of n terms of a geometric progression is-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/shvIJ1A453LfFcis2XK3F5Jh8kkxYnpod2-oKi3CkIsFZ0xkVQVEmIafK8Dwv0SXEtTwxxdwYE1vGZhFCAQuLKmsSa3kf11FTgHa7oOcotRmg1UUD8fNBNL8D2afAKoWl4qG7i98\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>Hence the limit will be-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/bTpeClLdvo9JTxN6I8zqFeWs8oXxaN7mkXAQQyuZGDVkqRiPLSPjfbiRMnTj71ZF7dAKQnXldC6sfRCXcVGn1P9U7du44x_y7ubOVWdNOfkkWbT6Szmcz2tHw3-6UxjQpeano4w7\" alt=\"\"\/><\/figure><\/div>\n\n\n<p>So that the series is convergent.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">General properties of series<\/h2>\n\n\n\n<p>The general properties of series are-<\/p>\n\n\n\n<p>1. The nature of a series does not change by multiplication of all terms by a constant k.<\/p>\n\n\n\n<p>2. The nature of a series does not change by adding or deleting of a finite number of terms.<\/p>\n\n\n\n<p>Interested in learning about similar topics? 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That means the limit of a sequence Sn will be always finite in case of convergent sequence and series.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the convergence of sequence and series? - Goseeko blog\" \/>\n<meta property=\"og:description\" content=\"A sequence Sn is said to be convergent when it tends to a finite limit. That means the limit of a sequence Sn will be always finite in case of convergent sequence and series.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/\" \/>\n<meta property=\"og:site_name\" content=\"Goseeko blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/goseeko\" \/>\n<meta property=\"article:published_time\" content=\"2021-08-03T04:42:20+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-12-07T16:50:24+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.goseeko.com\/blog\/wp-content\/uploads\/2021\/07\/whiteboard-with-formulas-scaled-1.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"2560\" \/>\n\t<meta property=\"og:image:height\" content=\"1707\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Gunjan\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@goseeko\" \/>\n<meta name=\"twitter:site\" content=\"@goseeko\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Gunjan\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"9 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/\"},\"author\":{\"name\":\"Gunjan\",\"@id\":\"https:\/\/www.goseeko.com\/blog\/#\/schema\/person\/843a7ac71fc4ae8c177dbb7820f2dc9c\"},\"headline\":\"What is the convergence of sequence and series?\",\"datePublished\":\"2021-08-03T04:42:20+00:00\",\"dateModified\":\"2025-12-07T16:50:24+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/\"},\"wordCount\":716,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/www.goseeko.com\/blog\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2021\/07\/whiteboard-with-formulas-scaled-1.jpg?fit=2560%2C1707&ssl=1\",\"articleSection\":[\"Maths\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/\",\"url\":\"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/\",\"name\":\"What is the convergence of sequence and series? - Goseeko blog\",\"isPartOf\":{\"@id\":\"https:\/\/www.goseeko.com\/blog\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.goseeko.com\/blog\/what-is-the-convergence-of-sequence-and-series\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/i0.wp.com\/www.goseeko.com\/blog\/wp-content\/uploads\/2021\/07\/whiteboard-with-formulas-scaled-1.jpg?fit=2560%2C1707&ssl=1\",\"datePublished\":\"2021-08-03T04:42:20+00:00\",\"dateModified\":\"2025-12-07T16:50:24+00:00\",\"description\":\"A sequence Sn is said to be convergent when it tends to a finite limit. 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