{"id":925,"date":"2025-06-20T17:23:02","date_gmt":"2025-06-20T17:23:02","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/?post_type=chapter&#038;p=925"},"modified":"2025-12-17T16:40:03","modified_gmt":"2025-12-17T16:40:03","slug":"introduction-to-power-series-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/introduction-to-power-series-apply-it\/","title":{"raw":"Introduction to Power Series: Apply It","rendered":"Introduction to Power Series: Apply It"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li>Recognize power series and when they converge<\/li>\r\n \t<li>Find where a power series converges and where it doesn't<\/li>\r\n \t<li>Use power series to write functions<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Data Science Modeling<\/h2>\r\n<p class=\"whitespace-normal break-words\">Data scientists frequently use power series to model complex phenomena and create predictive algorithms. Power series provide flexible mathematical tools for approximating functions, analyzing convergence behavior, and building machine learning models. Understanding where these series converge is crucial for determining the valid input ranges for your models.<\/p>\r\n<p class=\"whitespace-normal break-words\">You're working as a data scientist developing predictive models for various business applications. Each model uses power series representations that need to be analyzed for convergence to ensure reliable predictions within specific parameter ranges.<\/p>\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313542[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313544[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313593[\/ohm_question]<\/p>\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">\r\n<p class=\"whitespace-normal break-words\">[ohm_question hide_question_numbers=1]313594[\/ohm_question]<\/p>\r\n\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li>Recognize power series and when they converge<\/li>\n<li>Find where a power series converges and where it doesn&#8217;t<\/li>\n<li>Use power series to write functions<\/li>\n<\/ul>\n<\/section>\n<h2>Data Science Modeling<\/h2>\n<p class=\"whitespace-normal break-words\">Data scientists frequently use power series to model complex phenomena and create predictive algorithms. Power series provide flexible mathematical tools for approximating functions, analyzing convergence behavior, and building machine learning models. Understanding where these series converge is crucial for determining the valid input ranges for your models.<\/p>\n<p class=\"whitespace-normal break-words\">You&#8217;re working as a data scientist developing predictive models for various business applications. Each model uses power series representations that need to be analyzed for convergence to ensure reliable predictions within specific parameter ranges.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313542\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313542&theme=lumen&iframe_resize_id=ohm313542&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313544\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313544&theme=lumen&iframe_resize_id=ohm313544&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313593\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313593&theme=lumen&iframe_resize_id=ohm313593&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\">\n<p class=\"whitespace-normal break-words\"><iframe loading=\"lazy\" id=\"ohm313594\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313594&theme=lumen&iframe_resize_id=ohm313594&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/section>\n","protected":false},"author":15,"menu_order":9,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":673,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/925"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":14,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/925\/revisions"}],"predecessor-version":[{"id":2514,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/925\/revisions\/2514"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/673"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/925\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=925"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=925"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=925"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=925"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}