{"id":283,"date":"2018-05-17T08:44:16","date_gmt":"2018-05-17T06:44:16","guid":{"rendered":"http:\/\/clases.jesussoto.es\/?p=283"},"modified":"2018-05-17T17:00:17","modified_gmt":"2018-05-17T15:00:17","slug":"mad-teorema-del-binomio","status":"publish","type":"post","link":"https:\/\/curso17.jesussoto.es\/?p=283","title":{"rendered":"MAD: Teorema del binomio"},"content":{"rendered":"<p>El pasado d\u00eda vimos el n\u00famero binomial y dejamos las bases puestas para enunciar el <a href=\"http:\/\/es.wikipedia.org\/wiki\/Teorema_del_binomio\" target=\"_blank\">Teorema del Binomio<\/a>:<\/p>\n<p>$$(x+y)^n=\\sum_{k=0}^n {n \\choose k}x^{n-k} y^k$$<\/p>\n<p>Con este teorema podemos hacer f\u00e1ciles ejercicios que resultan dif\u00edciles en su planteamiento.<\/p>\n<p>Un resultado interesante es el siguiente. Utilizando el teorema del binomio podemos ver que<\/p>\n<p>$$(1+x)^n=\\sum_{k=0}^n {n \\choose k}x^{k}$$<\/p>\n<table id=\"yzpi\" width=\"100%\" border=\"0\" cellspacing=\"0\" cellpadding=\"3\" bgcolor=\"#999999\">\n<tbody>\n<tr>\n<td width=\"100%\"><strong>Ejercicio:<\/strong>Calcular cuanto suma para todo $n\\in\\mathbb{N}$ $${n\\choose 0}-{n\\choose 1}+{n\\choose 2}-{n\\choose 3}+\\cdots+(-1)^{i+1}{n\\choose i}+\\cdots+(-1)^{n+1}{n\\choose n}$$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>El pasado d\u00eda vimos el n\u00famero binomial y dejamos las bases puestas para enunciar el Teorema del Binomio: $$(x+y)^n=\\sum_{k=0}^n {n \\choose k}x^{n-k} y^k$$ Con este teorema podemos hacer f\u00e1ciles ejercicios que resultan dif\u00edciles en su planteamiento. Un resultado interesante es el siguiente. Utilizando el teorema del binomio podemos ver que $$(1+x)^n=\\sum_{k=0}^n {n \\choose k}x^{k}$$ Ejercicio:Calcular&hellip; <a class=\"more-link\" href=\"https:\/\/curso17.jesussoto.es\/?p=283\">Seguir leyendo <span class=\"screen-reader-text\">MAD: Teorema del binomio<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[5],"tags":[],"_links":{"self":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/283"}],"collection":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=283"}],"version-history":[{"count":4,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/283\/revisions"}],"predecessor-version":[{"id":301,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/283\/revisions\/301"}],"wp:attachment":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=283"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=283"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=283"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}