{"id":5287,"date":"2017-08-24T14:28:09","date_gmt":"2017-08-24T19:28:09","guid":{"rendered":"http:\/\/blog.espol.edu.ec\/telg1001\/?p=5287"},"modified":"2026-04-18T12:26:54","modified_gmt":"2026-04-18T17:26:54","slug":"sumatorias-tabla","status":"publish","type":"post","link":"https:\/\/blog.espol.edu.ec\/algoritmos101\/ss-u07\/sumatorias-tabla\/","title":{"rendered":"7.6.1 Sumatorias - Tabla"},"content":{"rendered":"\n

Referencia<\/strong><\/em>: Lathi Sec. B p54<\/p>\n\n\n\n

B.8-3 Sumatorias<\/p>\n\n\n \\sum_{k=m}^{n} r^k = \\frac{r^{n+1}-r^m}{r-1} \\texttt{ , } r\\neq 1<\/span>\n\n\n \\sum_{k=0}^{n} k = \\frac{n(n+1)}{2}<\/span>\n\n\n \\sum_{k=0}^{n} k^2 = \\frac{n(n+1)(2n+1)}{6}<\/span>\n\n\n \\sum_{k=0}^{n} k r^k = \\frac{r+[n(r-1)-1]r^{n+1}}{(r-1)^2} \\texttt{ , } r\\neq 1 <\/span>\n\n\n \\sum_{k=0}^{n} k^2 r^k = \\frac{r[(1+r)(1-r^n)-2n(1-r)r^n - n^2(1-r)^2 r^n] }{(1-r)^3} \\texttt{ , } r\\neq 1 <\/span>\n\n\n\n

\n\n\n\n

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

Series Finitas <\/h2>\n\n\n \\sum_{n=1}^{N} n = \\frac{N(N+1)}{2} <\/span>\n\n\n \\sum_{n=1}^{N} n^2 = \\frac{N(N+1)(2N+1)}{6} <\/span>\n\n\n \\sum_{n=1}^{N} n^3 = \\frac{N^2(N+1)^2}{4} <\/span>\n\n\n \\sum_{n=0}^{N} a^n = \\frac{a^{N+1}-1}{a-1} <\/span>\n\n\n \\sum_{n=0}^{N} \\frac{N!}{n!(N-n)!}x^n y^{N-n} = (x+y)^N <\/span>\n\n\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\n\n <\/span>\n\n\n\n
\n\n\n \\sum_{n=0}^{N} {N \\choose k} a^{N-k}b^{k} = (a+b)^N, <\/span>\n\n\n donde: {N \\choose k} = \\frac{N!}{(N-k)!k!} <\/span>\n\n\n\n
\n\n\n\n

Series Infinitas <\/h2>\n\n\n\n

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

\n\n\n\n

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

\n\n\n\n

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

Referencia: Lathi Sec. B p54 B.8-3 Sumatorias 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-ss-unidades","format":"standard","meta":{"footnotes":""},"categories":[177],"tags":[],"class_list":["post-5287","post","type-post","status-publish","format-standard","hentry","category-ss-u07"],"_links":{"self":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/5287","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=5287"}],"version-history":[{"count":6,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/5287\/revisions"}],"predecessor-version":[{"id":24357,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/posts\/5287\/revisions\/24357"}],"wp:attachment":[{"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/media?parent=5287"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/categories?post=5287"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.espol.edu.ec\/algoritmos101\/wp-json\/wp\/v2\/tags?post=5287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}