[{"data":1,"prerenderedAt":141},["ShallowReactive",2],{"\u002Fpublic\u002Ftopics\u002Falgebra\u002Fsucesiones-y-series?{}":3,"topics-with-content:algebra":118},{"course":4,"topic":12,"counts":17,"universities":22,"channels":34,"sampleQuestions":71,"sameName":114},{"id":5,"slug":6,"name":7,"shortName":8,"area":9,"icon":10,"sortOrder":11},2,"algebra","Álgebra","Álg.","math","i-lucide-variable",1,{"id":13,"courseId":5,"slug":14,"name":15,"sortOrder":16},218,"sucesiones-y-series","Sucesiones y series",17,{"topicId":13,"courseId":5,"questions":18,"classes":19,"videos":20,"minutes":21},30,108,84,1549,[23,31],{"universityId":11,"questions":24,"years":25},18,[26,27,28,29,30],2026,2025,2024,2023,2022,{"universityId":5,"questions":32,"years":33},12,[26,27,28,29,30],[35,38,41,44,47,50,53,56,59,62,64,67,69],{"name":36,"classes":37},"Alberto Cruz",26,{"name":39,"classes":40},"Academia ipluton",15,{"name":42,"classes":43},"Academia Grupo Ciencias",13,{"name":45,"classes":46},"Academias Aduni y César Vallejo",10,{"name":48,"classes":49},"Ciclo Uni-San Marcos",9,{"name":51,"classes":52},"Trilce Multimedia",7,{"name":54,"classes":55},"Pamer Corporación Educativa",6,{"name":57,"classes":58},"Academia Internet",5,{"name":60,"classes":61},"META VILLARREAL",4,{"name":63,"classes":61},"Salón Sapiens",{"name":65,"classes":66},"Academia_Pitagoras",3,{"name":68,"classes":66},"CEPRE UNMSM",{"name":70,"classes":66},"Saco Oliveros",[72,97],{"id":73,"courseId":5,"topicId":13,"pastExamId":74,"stem":75,"options":76,"correctKey":84,"explanation":92,"difficulty":66,"status":93,"source":94,"stats":95},1646,198,"Sea $\\{a_{n}\\}$ una sucesión que converge a un número real $a>1$ y $\\sum b_{n}$ una serie que converge a 1. Calcule\n$\\displaystyle\\lim_{n\\to+\\infty}\\left[5a_{n}^{2}(1-b_{n})+2a_{n}b_{n}\\right]$",[77,80,83,86,89],{"key":78,"text":79},"A","0",{"key":81,"text":82},"B","$2a$",{"key":84,"text":85},"C","$5a^{2}$",{"key":87,"text":88},"D","$7a^{2}$",{"key":90,"text":91},"E","$5a^{2}+2a$","","published","UNI 2026-1 · Matemática",{"attempts":96,"accuracy":96},0,{"id":98,"courseId":5,"topicId":13,"pastExamId":99,"stem":100,"options":101,"correctKey":78,"explanation":92,"difficulty":66,"status":93,"source":112,"stats":113},1813,201,"Se establece la expresión $S$, la cual presenta una cantidad ilimitada de sumandos, según como se muestra.\n$$S=\\frac{3}{5}+\\frac{2}{5^2}+\\frac{4}{5^3}+\\frac{2}{5^4}+\\frac{4}{5^5}+\\frac{2}{5^6}+\\frac{4}{5^7}+\\ldots$$\nCalcule el valor de $120S$.",[102,104,106,108,110],{"key":78,"text":103},"86",{"key":81,"text":105},"87",{"key":84,"text":107},"88",{"key":87,"text":109},"89",{"key":90,"text":111},"90","UNI 2026-2 · Matemática",{"attempts":96,"accuracy":96},[115],{"courseName":116,"path":117},"Aritmética","\u002Fcursos\u002Faritmetica\u002Fsucesiones-y-series",[99,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,13,135,136,137,138,139,140],202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,219,220,221,223,225,226,1791501527119]