{"id":155734,"date":"2022-03-26T00:58:30","date_gmt":"2022-03-25T19:28:30","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/principle-of-mathematical-induction\/"},"modified":"2025-02-11T10:48:28","modified_gmt":"2025-02-11T05:18:28","slug":"maths-principle-of-mathematical-induction","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/principle-of-mathematical-induction\/","title":{"rendered":"Principles of Mathematical Induction"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/principle-of-mathematical-induction\/#Explain_in_Detail_Properties_of_Mathematical_Induction\" title=\"Explain in Detail: Properties of Mathematical Induction\">Explain in Detail: Properties of Mathematical Induction<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/principle-of-mathematical-induction\/#Principles_of_Mathematical_Induction_Examples\" title=\"Principles of Mathematical Induction Examples\">Principles of Mathematical Induction Examples<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><strong>Principles of Mathematical Induction:<\/strong> Mathematical induction is a process of reasoning that allows us to establish a result for a given sequence of numbers. This result is then used to prove a statement about the sequence.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Explain_in_Detail_Properties_of_Mathematical_Induction\"><\/span><span style=\"font-size: 18pt; color: #0000ff;\"><span style=\"color: #000000;\">Explain in Detail: <\/span>Properties of Mathematical Induction<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The basis of mathematical induction is the fact that if a statement is true for the first number in a sequence, it is also true for the second number. This is because the second number is just a copy of the first number, with one addition or subtraction.<\/p>\n<p>To use mathematical induction, we first need to come up with a statement that we want to prove. This statement can be about a sequence of numbers, or about a property that the numbers in the sequence have.<\/p>\n<p>We then need to come up with a base case, which is a number for which we know the statement is definitely true. We can then use mathematical induction to prove the statement is true for all other numbers in the sequence.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155733 size-medium\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/principle-of-mathematical-induction-300x212.jpg\" alt=\"Principles of Mathematical Induction\" width=\"300\" height=\"212\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/principle-of-mathematical-induction-300x212.jpg?v=1648236507 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/principle-of-mathematical-induction.jpg?v=1648236507 606w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Principles_of_Mathematical_Induction_Examples\"><\/span><span style=\"color: #0000ff; font-size: 14pt;\">Principles of Mathematical Induction Examples<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The principle of mathematical induction is a logical principle that states that a statement is true for all natural numbers if it is true for the first natural number and for every natural number that follows the first natural number.<\/p>\n<p>Some examples of how the principle of mathematical induction can be used are as follows:<\/p>\n<p>&#8211; To show that a statement is true for all natural numbers, it is first necessary to show that the statement is true for the first natural number.<\/p>\n<p>&#8211; Then, it is necessary to show that the statement is true for every natural number that follows the first natural number.<\/p>\n<p>&#8211; If both of these steps can be shown to be true, then the statement is said to be true for all natural numbers.<\/p>\n<p>The principle of mathematical induction is a logical principle that is used to prove a statement is true for all natural numbers. The principle is based on the assumption that if a statement is true for a particular natural number, then it is also true for the next natural number. The principle can be used to prove a statement is true for all positive integers.<\/p>\n<p>The principle of mathematical induction can be illustrated with the following example.<\/p>\n<p>Example:<\/p>\n<p>Prove that the statement &#8220;2 + 3 = 5&#8221; is true for all natural numbers.<\/p>\n<p>The statement &#8220;2 + 3 = 5&#8221; is true for the natural number 2. The principle of induction can be used to show that the statement is also true for the next natural number, which is 3.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Principles of Mathematical Induction: Mathematical induction is a process of reasoning that allows us to establish a result for a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Principles of Mathematical Induction","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about the Principles of Mathematical Induction in detail along with examples explained in this article.","custom_permalink":"maths\/principle-of-mathematical-induction\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Principles of Mathematical Induction - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about the Principles of Mathematical Induction in detail along with examples explained in this article.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/principle-of-mathematical-induction\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Principles of Mathematical Induction - 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