{"id":3279,"date":"2021-06-17T17:42:54","date_gmt":"2021-06-17T15:42:54","guid":{"rendered":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/?p=3279"},"modified":"2021-11-07T10:56:04","modified_gmt":"2021-11-07T09:56:04","slug":"numero-e-y-factoriales","status":"publish","type":"post","link":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/numero-e-y-factoriales\/","title":{"rendered":"N\u00famero e y factoriales"},"content":{"rendered":"<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">A partir del desarrollo en serie de la funci\u00f3n e<sup>x<\/sup>:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3280\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/n\u00famero_e_2.png\" alt=\"\" width=\"364\" height=\"59\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/n\u00famero_e_2.png 364w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/n\u00famero_e_2-300x49.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">se puede obtener cualquier potencia del n\u00famero e, en particular, el mismo <strong>n\u00famero e<\/strong> se obtiene como suma de los inversos de los factoriales de todos los n\u00fameros naturales incluido el 0 (0!=1).<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3282\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/n\u00famero_e_3.png\" alt=\"\" width=\"370\" height=\"59\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/n\u00famero_e_3.png 370w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/n\u00famero_e_3-300x48.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Utilizando el emulador de la calculadora Classwiz fx-570SP X Iberia, podemos obtener el valor de la suma hasta 69 sumandos, pero con la suma de los primeros veinte t\u00e9rminos, los nueve decimales que aparecen ya coinciden los los del n\u00famero e:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3759\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/num_e_1.png\" alt=\"\" width=\"340\" height=\"69\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/num_e_1.png 340w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/num_e_1-300x61.png 300w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><\/p>\n<p style=\"text-align: justify\"><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Utilizando la vista \u00abC\u00e1lculo Simb\u00f3lico\u00bb de Geogebra, al sumar cien t\u00e9rminos de la serie, coinciden todas las cifras decimales:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3766\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/num_e_4.png\" alt=\"\" width=\"788\" height=\"58\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/num_e_4.png 788w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/num_e_4-300x22.png 300w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/num_e_4-768x57.png 768w\" sizes=\"(max-width: 788px) 100vw, 788px\" \/><\/p>\n<p><span style=\"font-family: 'times new roman', times, serif;font-size: 14pt\">Tambi\u00e9n se obtiene e<sup>-1<\/sup>&nbsp; como:<\/span><\/p>\n<p style=\"text-align: center\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3283\" src=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/n\u00famero_e_4.png\" alt=\"\" width=\"383\" height=\"62\" srcset=\"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/n\u00famero_e_4.png 383w, https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/files\/2021\/06\/n\u00famero_e_4-300x49.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>A partir del desarrollo en serie de la funci\u00f3n ex: se puede obtener cualquier potencia del n\u00famero e, en particular, el mismo n\u00famero e se obtiene como suma de los inversos de los factoriales&#46;&#46;&#46;<\/p>\n","protected":false},"author":7927,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[2075218],"tags":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/3279"}],"collection":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/users\/7927"}],"replies":[{"embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/comments?post=3279"}],"version-history":[{"count":7,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/3279\/revisions"}],"predecessor-version":[{"id":3768,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/posts\/3279\/revisions\/3768"}],"wp:attachment":[{"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/media?parent=3279"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/categories?post=3279"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogsaverroes.juntadeandalucia.es\/recursosdematematicas\/wp-json\/wp\/v2\/tags?post=3279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}