{"id":2221,"date":"2011-03-02T19:31:05","date_gmt":"2011-03-02T17:31:05","guid":{"rendered":"http:\/\/laaventuradelasmatematicas.jesussoto.es\/?p=2221"},"modified":"2013-10-05T19:45:14","modified_gmt":"2013-10-05T17:45:14","slug":"jacob-bernoulli-y-1-11-11","status":"publish","type":"post","link":"https:\/\/pimedios.jesussoto.es\/?p=2221","title":{"rendered":"Jacob Bernoulli  y 1-1+1-1+1-&#8230;"},"content":{"rendered":"<p><a href=\"http:\/\/pimedios.es\/wp-content\/uploads\/2011\/02\/jacobBernoulli.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-2222\" title=\"jacobBernoulli\" src=\"http:\/\/pimedios.es\/wp-content\/uploads\/2011\/02\/jacobBernoulli-300x217.jpg\" alt=\"\" width=\"300\" height=\"217\" \/><\/a> Ya hemos hablado de esta serie que Oresmes sac\u00f3 a la palestra. Leibniz lo intent\u00f3 y, equivocadamente, lleg\u00f3 a la conclusi\u00f3n de que resultaba 1\/2.<\/p>\n<p>No fue el \u00fanico, Jacob Bernoulli(1654-1705) lleg\u00f3 al mismo resultado. \u00c9l consider\u00f3<\/p>\n<p>$$\\frac{l}{m+n}=\\frac{l}{m}\\left(1+\\frac{n}{m}\\right)^{-1}=\\frac{l}{m}-\\frac{ln}{m^2}+\\frac{ln^2}{m^3}-&#8230;$$<br \/>\nque cuando $m=n$ nos da<br \/>\n$$\\frac{l}{2m}=\\frac{l}{m}-\\frac{l}{m}+\\frac{l}{m}-&#8230;$$<\/p>\n<p>El paso para obtener la sucesi\u00f3n de Oresme es evidente, para \u00e9l.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ya hemos hablado de esta serie que Oresmes sac\u00f3 a la palestra. Leibniz lo intent\u00f3 y, equivocadamente, lleg\u00f3 a la conclusi\u00f3n de que resultaba 1\/2. No fue el \u00fanico, Jacob Bernoulli(1654-1705) lleg\u00f3 al mismo resultado. \u00c9l consider\u00f3 $$\\frac{l}{m+n}=\\frac{l}{m}\\left(1+\\frac{n}{m}\\right)^{-1}=\\frac{l}{m}-\\frac{ln}{m^2}+\\frac{ln^2}{m^3}-&#8230;$$ que cuando $m=n$ nos da $$\\frac{l}{2m}=\\frac{l}{m}-\\frac{l}{m}+\\frac{l}{m}-&#8230;$$ El paso para obtener la sucesi\u00f3n de Oresme es evidente, para&hellip; <a class=\"more-link\" href=\"https:\/\/pimedios.jesussoto.es\/?p=2221\">Seguir leyendo <span class=\"screen-reader-text\">Jacob Bernoulli  y 1-1+1-1+1-&#8230;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[190,279],"class_list":["post-2221","post","type-post","status-publish","format-standard","hentry","category-historia","tag-jacob-bernoulli","tag-oresmes","entry"],"_links":{"self":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/2221","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2221"}],"version-history":[{"count":1,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/2221\/revisions"}],"predecessor-version":[{"id":3948,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/2221\/revisions\/3948"}],"wp:attachment":[{"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2221"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2221"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2221"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}