{"id":21998,"date":"2016-11-18T07:20:39","date_gmt":"2016-11-18T12:20:39","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/estg1003\/?p=659"},"modified":"2026-04-04T11:28:36","modified_gmt":"2026-04-04T16:28:36","slug":"expansiones-de-series","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/stp-recursos\/expansiones-de-series\/","title":{"rendered":"Expansiones de Series"},"content":{"rendered":"

Referencia<\/em><\/strong>: Leon W Couch Ap\u00e9ndice p658<\/p>\n

Series Finitas <\/strong><\/p>\n \\sum_{n=1}^{N} n = \\frac{N(N+1)}{2} <\/span>\n \\sum_{n=1}^{N} n^2 = \\frac{N(N+1)(2N+1)}{6} <\/span>\n \\sum_{n=1}^{N} n^3 = \\frac{N^2(N+1)^2}{4} <\/span>\n \\sum_{n=0}^{N} a^n = \\frac{a^{N+1}-1}{a-1} <\/span>\n \\sum_{n=0}^{N} \\frac{N!}{n!(N-n)!}x^n y^{N-n} = (x+y)^N <\/span>\n \\sum_{n=0}^{N} e^{j(\\theta+n\\phi)} = \\frac{sen \\left[(N+1) \\frac{\\phi}{2}\\right] }{sen \\left( \\frac{\\phi}{2} \\right)} e^{j [ \\theta + \\left( N \\frac{\\phi}{2} \\right) ]}<\/span>\n <\/span>\n

\n \\sum_{n=0}^{N} {N \\choose k} a^{N-k}b^{k} = (a+b)^N, <\/span>\n donde: {N \\choose k} = \\frac{N!}{(N-k)!k!} <\/span>\n
\n

Series Infinitas <\/strong><\/p>\n

Serie de Taylor<\/p>\n f(x) = \\sum_{n=0}^{\\infty} \\left( \\frac{f^{(n)}(a)}{n!} \\right) (x-a)^n <\/span>\n

\n

Serie de Fourier<\/p>\n f(x) = \\sum_{n=-\\infty}^{\\infty} c_n e^{jn\\omega_0 x} <\/span>\n a\\leq x \\leq (a+T) <\/span>\n donde: c_n = \\frac{1}{T} \\int_{a}^{a+T} f(x) e^{-jn\\omega_0 x} dx <\/span>\n \\omega_o = \\frac{2\\pi}{T} <\/span>\n

\n

otras series<\/p>\n e^x = \\sum_{n=0}^{\\infty} \\frac{x^n}{n!} <\/span>\n sen(x) = \\sum_{n=0}^{\\infty} \\frac{(-1)^n x^{2n+1}}{(2n+1)!} <\/span>\n cos(x) = \\sum_{n=0}^{\\infty} \\frac{(-1)^n x^{2n}}{(2n)!} <\/span>\n","protected":false},"excerpt":{"rendered":"

Referencia: Leon W Couch Ap\u00e9ndice p658 Series Finitas Series Infinitas Serie de Taylor Serie de Fourier otras series<\/p>\n","protected":false},"author":8043,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"wp-custom-template-entrada-stp-unidades","format":"standard","meta":{"footnotes":""},"categories":[205],"tags":[],"class_list":["post-21998","post","type-post","status-publish","format-standard","hentry","category-stp-recursos"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/21998","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/users\/8043"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/comments?post=21998"}],"version-history":[{"count":1,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/21998\/revisions"}],"predecessor-version":[{"id":22278,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/21998\/revisions\/22278"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=21998"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=21998"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=21998"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}