{"id":647,"date":"2012-04-01T00:12:58","date_gmt":"2012-03-31T23:12:58","guid":{"rendered":"http:\/\/nosolomates.es\/?page_id=647"},"modified":"2012-04-01T00:12:58","modified_gmt":"2012-03-31T23:12:58","slug":"series-de-fibonacci","status":"publish","type":"page","link":"https:\/\/nosolomates.es\/?page_id=647","title":{"rendered":"Series de Fibonacci"},"content":{"rendered":"<p>Herramienta para obtener series de Fibonacci, series en las que cada n\u00famero es la suma de los dos anteriores. Introduce en las casillas los dos primeros t\u00e9rminos de la serie y cu\u00e1ntos quieres hallar. Despu\u00e9s pulsa &#8220;Mostrar n\u00fameros&#8221;.<\/p>\n<p><center><\/p>\n<div id=\"utilidades\"><h7><iframe loading=\"lazy\" src=\"web\/fibonacci.htm\" width=\"470\" height=\"520\" scrolling=\"auto\" frameborder=\"0\"><\/p>\n<p>Texto alternativo para browsers que no aceptan iframes.<\/p>\n<p>    <\/iframe><\/h7><\/div>\n<p><\/center><br \/>\n<\/p>\n<h1>Explicaci\u00f3n:<\/h1>\n<p>Una sucesi\u00f3n de Fibonacci es aquella cuya ley de recurrencia es:<br \/>\n<center><\/p>\n<p style=\"font-size: 1.4em;\">a<sub>n<\/sub> = a<sub>n-1<\/sub> + a<sub>n-2<\/sub><\/b><\/p>\n<p><\/center><\/p>\n<p>Es decir, cada t\u00e9rmino de la sucesi\u00f3n se obtiene sumando los dos anteriores. Para empezar a construirla necesitamos, por tanto, dos n\u00fameros de partida, a<sub>1<\/sub> y a<sub>2<\/sub>. De esta forma, a<sub>3<\/sub> ser\u00eda a<sub>2<\/sub> + a<sub>1<\/sub> ; a<sub>4<\/sub> ser\u00eda a<sub>3<\/sub> + a<sub>2<\/sub> y as\u00ed sucesivamente.<\/p>\n<p>La m\u00e1s conocida es la que tiene a<sub>1<\/sub> = 1 &nbsp;y &nbsp;a<sub>2<\/sub> = 1, cuyos t\u00e9rminos son:<\/p>\n<p><center><\/p>\n<p class=\"bold\">1 &nbsp;1 &nbsp;2 &nbsp;3 &nbsp;5 &nbsp;8 &nbsp;13 &nbsp;21 &nbsp;34 &nbsp;55 &nbsp;89 &nbsp;144 &nbsp;233 &nbsp;377 &#8230;<\/p>\n<p><\/center><\/p>\n<p>n\u00fameros que son conocidos como N\u00fameros de Fibonacci.<\/p>\n<p>Los t\u00e9rminos de cualquier sucesi\u00f3n de Fibonacci tienen la particularidad de que el cociente entre dos t\u00e9rminos consecutivos se aproxima al N\u00famero de Oro (1.6180339887499&#8230;), es decir, el l\u00edmite de los cocientes a<sub>n+1<\/sub>\/a<sub>n<\/sub> tiende al N\u00famero de Oro cuando n tiende a infinito.<\/p>\n<p>Adem\u00e1s, las series de Fibonacci cumplen otras curiosas propiedades, como por ejemplo, que la suma de n t\u00e9rminos es igual al t\u00e9rmino n+2 menos uno:<\/p>\n<p><center><\/p>\n<p style=\"font-size: 1.4em;\">a<sub>1<\/sub> + a<sub>2<\/sub> + a<sub>3<\/sub> + a<sub>4<\/sub> + &#8230;.. + a<sub>n-1<\/sub> + a<sub>n<\/sub> = a<sub>n+2<\/sub> &#8211; 1<\/p>\n<p><\/center><\/p>\n<div><\/br>&nbsp;<\/div>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-official sd-sharing\"><div class=\"sd-content\"><ul><li class=\"share-facebook\"><div class=\"fb-share-button\" data-href=\"https:\/\/nosolomates.es\/?page_id=647\" data-layout=\"button_count\"><\/div><\/li><li class=\"share-twitter\"><a href=\"https:\/\/twitter.com\/share\" class=\"twitter-share-button\" data-url=\"https:\/\/nosolomates.es\/?page_id=647\" data-text=\"Series de Fibonacci\"  >Tweet<\/a><\/li><li class=\"share-linkedin\"><div class=\"linkedin_button\"><script type=\"in\/share\" data-url=\"https:\/\/nosolomates.es\/?page_id=647\" data-counter=\"right\"><\/script><\/div><\/li><li class=\"share-pinterest\"><div class=\"pinterest_button\"><a href=\"https:\/\/www.pinterest.com\/pin\/create\/button\/?url=https%3A%2F%2Fnosolomates.es%2F%3Fpage_id%3D647&#038;media=https%3A%2F%2Fsecure.gravatar.com%2Favatar%2Fc9ba1828908559b850337a4baa073367%3Fs%3D96%26d%3Dmm%26r%3Dg&#038;description=Series%20de%20Fibonacci\" data-pin-do=\"buttonPin\" data-pin-config=\"beside\"><img src=\"\/\/assets.pinterest.com\/images\/pidgets\/pinit_fg_en_rect_gray_20.png\" \/><\/a><\/div><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Herramienta para obtener series de Fibonacci, series en las que cada n\u00famero es la suma de los dos anteriores. Introduce en las casillas los dos primeros t\u00e9rminos de la serie y cu\u00e1ntos quieres hallar. Despu\u00e9s pulsa &#8220;Mostrar n\u00fameros&#8221;. Texto alternativo &hellip; <a href=\"https:\/\/nosolomates.es\/?page_id=647\">Sigue leyendo <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n<div class=\"sharedaddy sd-sharing-enabled\"><div class=\"robots-nocontent sd-block sd-social sd-social-official sd-sharing\"><div class=\"sd-content\"><ul><li class=\"share-facebook\"><div class=\"fb-share-button\" data-href=\"https:\/\/nosolomates.es\/?page_id=647\" data-layout=\"button_count\"><\/div><\/li><li class=\"share-twitter\"><a href=\"https:\/\/twitter.com\/share\" class=\"twitter-share-button\" data-url=\"https:\/\/nosolomates.es\/?page_id=647\" data-text=\"Series de Fibonacci\"  >Tweet<\/a><\/li><li class=\"share-linkedin\"><div class=\"linkedin_button\"><script type=\"in\/share\" data-url=\"https:\/\/nosolomates.es\/?page_id=647\" data-counter=\"right\"><\/script><\/div><\/li><li class=\"share-pinterest\"><div class=\"pinterest_button\"><a href=\"https:\/\/www.pinterest.com\/pin\/create\/button\/?url=https%3A%2F%2Fnosolomates.es%2F%3Fpage_id%3D647&#038;media=https%3A%2F%2Fsecure.gravatar.com%2Favatar%2Fc9ba1828908559b850337a4baa073367%3Fs%3D96%26d%3Dmm%26r%3Dg&#038;description=Series%20de%20Fibonacci\" data-pin-do=\"buttonPin\" data-pin-config=\"beside\"><img src=\"\/\/assets.pinterest.com\/images\/pidgets\/pinit_fg_en_rect_gray_20.png\" \/><\/a><\/div><\/li><li class=\"share-end\"><\/li><\/ul><\/div><\/div><\/div>","protected":false},"author":1,"featured_media":0,"parent":623,"menu_order":9,"comment_status":"open","ping_status":"open","template":"","meta":{"jetpack_post_was_ever_published":false,"footnotes":""},"jetpack_shortlink":"https:\/\/wp.me\/P9BfV-ar","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/647"}],"collection":[{"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/nosolomates.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=647"}],"version-history":[{"count":1,"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/647\/revisions"}],"predecessor-version":[{"id":648,"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/647\/revisions\/648"}],"up":[{"embeddable":true,"href":"https:\/\/nosolomates.es\/index.php?rest_route=\/wp\/v2\/pages\/623"}],"wp:attachment":[{"href":"https:\/\/nosolomates.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}