{"id":279,"date":"2018-05-11T09:01:03","date_gmt":"2018-05-11T07:01:03","guid":{"rendered":"http:\/\/clases.jesussoto.es\/?p=279"},"modified":"2018-05-11T09:03:26","modified_gmt":"2018-05-11T07:03:26","slug":"mad-numero-binomial","status":"publish","type":"post","link":"https:\/\/curso17.jesussoto.es\/?p=279","title":{"rendered":"MAD: N\u00famero binomial"},"content":{"rendered":"

Comenzamos definiendo el n\u00famero binomial ${n\\choose k}$, como el n\u00famero de subconjuntos con k<\/i> elementos, escogidos de un conjunto con n<\/i>. Esta definici\u00f3n coincide con la combinaciones, por ese motivo la f\u00f3rmula de calcularlo debe ser la misma
\n$$
\n{n\\choose k} = \\frac{ n(n-1)(n-2)\\cdots (n-k+1)}{1\\cdot 2\\cdot 3 \\cdots (k-1)\\cdot k}
\n$$
\nLos coeficientes binomiales cumple propiedades muy interesantes como
\n$$
\n\\binom{n}{k} = \\binom{n-1}{k-1} + \\binom{n-1}{k} \\quad \\mbox{para todos los n\u00fameros enteros }n,k>0.
\n$$
\nEsta propiedad es muy importante y aparece en el El teorema de Pascal<\/a>.<\/p>\n

\n

\"TrianguloPascalC.svg\"<\/a>
\n\u00abTrianguloPascalC<\/a>\u00bb por Drini<\/a> – Trabajo propio<\/span>. Disponible bajo la licencia CC BY-SA 3.0<\/a> v\u00eda Wikimedia Commons<\/a>.<\/p>\n<\/div>\n\n\n\n
Ejercicio:<\/strong>Probar que para todo $n\\in\\mathbb{N}$ es ${n\\choose 0}+{n\\choose 1}+{n\\choose 2}+\\cdots+{n\\choose n}=2^n$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Comenzamos definiendo el n\u00famero binomial ${n\\choose k}$, como el n\u00famero de subconjuntos con k elementos, escogidos de un conjunto con n. Esta definici\u00f3n coincide con la combinaciones, por ese motivo la f\u00f3rmula de calcularlo debe ser la misma $$ {n\\choose k} = \\frac{ n(n-1)(n-2)\\cdots (n-k+1)}{1\\cdot 2\\cdot 3 \\cdots (k-1)\\cdot k} $$ Los coeficientes binomiales cumple… Seguir leyendo MAD: N\u00famero binomial<\/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\/279"}],"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=279"}],"version-history":[{"count":3,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/279\/revisions"}],"predecessor-version":[{"id":282,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/279\/revisions\/282"}],"wp:attachment":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=279"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=279"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}