{"id":2575,"date":"2021-01-19T13:26:05","date_gmt":"2021-01-19T06:26:05","guid":{"rendered":"https:\/\/luckytruedev.com\/learning\/?p=2575"},"modified":"2021-01-19T13:26:07","modified_gmt":"2021-01-19T06:26:07","slug":"induksi-matematika","status":"publish","type":"post","link":"https:\/\/luckytruedev.com\/learning\/induksi-matematika\/","title":{"rendered":"Induksi Matematika"},"content":{"rendered":"\n<p>Induksi Matematika merupakan suatu teknik yang dikembangkan untuk membuktikan pernyataan.<\/p>\n\n\n\n<p>Pernyataan yang dimaksudkan dibatasi untuk pernyataan yang menyangkut bilangan bulat.<\/p>\n\n\n\n<p>Induksi Matematika digunakan untuk mengecek <strong>hasil proses <\/strong>yang terjadi secara berulang sesuai dengan pola tertentu<\/p>\n\n\n\n<p>Teknik untuk membuktikan proposisi dalam p(n), dengan domain bilangannya yaitu himpunan bilangan bulat positif.<\/p>\n\n\n\n<p>Suatu bukti dengan menggunakan induksi matematika bahwa \u201cp(n) benar untuk setiap n bilangan bulat positif \u201c<\/p>\n\n\n\n<p>terdiri dari tiga langkah: <\/p>\n\n\n\n<p>1.<strong>Langkah basis <\/strong>:<\/p>\n\n\n\n<p>Tunjukkan bahwa p(1) benar. <\/p>\n\n\n\n<p>2.<strong>Langkah induktif:<\/strong><\/p>\n\n\n\n<p>Tunjukkan bahwa p(n) dan p(n + 1) benar untuk setiap n.<\/p>\n\n\n\n<p>p(n) untuk suatu n tertentu disebut hipotesa induksi. <\/p>\n\n\n\n<p>3.<strong>Konklusi:<\/strong> &#8220;n p(n) bernilai benar.<\/p>\n\n\n\n<p><strong>Contoh :<\/strong><\/p>\n\n\n\n<p>Misalkan p(n) adalah pernyataan yang menyatakan :<\/p>\n\n\n\n<p>\u201cjumlah bilangan bulat positif dari 1 sampai n adalah n(n+1)\/2\u201d<\/p>\n\n\n\n<p>Misal untuk n =6 dan p(6) adalah jumlah bilangan bulat positif dari 1 sampai 6 adalah 6(6+1)\/2.<\/p>\n\n\n\n<p>Terlihat bahwa 1+2+3+4+5+6=21=6(7)\/2.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"571\" src=\"https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture1-22-1024x571.png\" alt=\"\" class=\"wp-image-2583\" srcset=\"https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture1-22-1024x571.png 1024w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture1-22-300x167.png 300w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture1-22-768x428.png 768w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture1-22-110x61.png 110w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture1-22-420x234.png 420w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture1-22-248x138.png 248w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture1-22-770x430.png 770w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture1-22.png 1459w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"383\" src=\"https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture2-21-1024x383.png\" alt=\"\" class=\"wp-image-2584\" srcset=\"https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture2-21-1024x383.png 1024w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture2-21-300x112.png 300w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture2-21-768x287.png 768w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture2-21-110x41.png 110w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture2-21-420x157.png 420w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture2-21-770x288.png 770w, https:\/\/luckytruedev.com\/learning\/wp-content\/uploads\/2021\/01\/Picture2-21.png 1425w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<div id=\"lucky-4137157426\" class=\"lucky-after-content lucky-entity-placement\"><script async src=\"\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-5605825534849002\" crossorigin=\"anonymous\"><\/script><ins class=\"adsbygoogle\" style=\"display:block;\" data-ad-client=\"ca-pub-5605825534849002\" \ndata-ad-slot=\"5317815257\" \ndata-ad-format=\"auto\" data-full-width-responsive=\"true\"><\/ins>\n<script> \n(adsbygoogle = window.adsbygoogle || []).push({}); \n<\/script>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Induksi Matematika merupakan suatu teknik yang dikembangkan untuk membuktikan pernyataan. Pernyataan yang dimaksudkan dibatasi untuk pernyataan yang menyangkut bilangan bulat. Induksi Matematika digunakan untuk mengecek hasil proses yang terjadi secara berulang sesuai dengan pola tertentu Teknik untuk membuktikan proposisi dalam p(n), dengan domain bilangannya yaitu himpunan bilangan bulat positif. Suatu bukti dengan menggunakan induksi matematika [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[347],"tags":[],"class_list":["post-2575","post","type-post","status-publish","format-standard","hentry","category-mtk-ltdv"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/luckytruedev.com\/learning\/wp-json\/wp\/v2\/posts\/2575","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/luckytruedev.com\/learning\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/luckytruedev.com\/learning\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/luckytruedev.com\/learning\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/luckytruedev.com\/learning\/wp-json\/wp\/v2\/comments?post=2575"}],"version-history":[{"count":1,"href":"https:\/\/luckytruedev.com\/learning\/wp-json\/wp\/v2\/posts\/2575\/revisions"}],"predecessor-version":[{"id":2585,"href":"https:\/\/luckytruedev.com\/learning\/wp-json\/wp\/v2\/posts\/2575\/revisions\/2585"}],"wp:attachment":[{"href":"https:\/\/luckytruedev.com\/learning\/wp-json\/wp\/v2\/media?parent=2575"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/luckytruedev.com\/learning\/wp-json\/wp\/v2\/categories?post=2575"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/luckytruedev.com\/learning\/wp-json\/wp\/v2\/tags?post=2575"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}