设数列{an}满足a1+3a2+3^2a3+.3^n-1×an=n/3,a∈N+.(1)求数列{an}的通项;(2)(选做题)设bn=n/an,求数列{bn}的前n项和sn周末家作.
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![设数列{an}满足a1+3a2+3^2a3+.3^n-1×an=n/3,a∈N+.(1)求数列{an}的通项;(2)(选做题)设bn=n/an,求数列{bn}的前n项和sn周末家作.](/uploads/image/z/1741144-40-4.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a1%2B3a2%2B3%5E2a3%2B.3%5En-1%C3%97an%3Dn%2F3%2Ca%E2%88%88N%2B.%EF%BC%881%EF%BC%89%E6%B1%82%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%EF%BC%9B%EF%BC%882%EF%BC%89%EF%BC%88%E9%80%89%E5%81%9A%E9%A2%98%EF%BC%89%E8%AE%BEbn%3Dn%2Fan%2C%E6%B1%82%E6%95%B0%E5%88%97%7Bbn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8Csn%E5%91%A8%E6%9C%AB%E5%AE%B6%E4%BD%9C.)
设数列{an}满足a1+3a2+3^2a3+.3^n-1×an=n/3,a∈N+.(1)求数列{an}的通项;(2)(选做题)设bn=n/an,求数列{bn}的前n项和sn周末家作.
设数列{an}满足a1+3a2+3^2a3+.3^n-1×an=n/3,a∈N+.
(1)求数列{an}的通项;
(2)(选做题)设bn=n/an,求数列{bn}的前n项和sn
周末家作.
设数列{an}满足a1+3a2+3^2a3+.3^n-1×an=n/3,a∈N+.(1)求数列{an}的通项;(2)(选做题)设bn=n/an,求数列{bn}的前n项和sn周末家作.
(1)a1+3a2+…+3^(n-2)an-1=(n-1)/3
a1+3a2+…+3^(n-1)an=(n-1)/3+3^(n-1)an=n/3
an=(1/3)^n.
(2)bn=n/an=n3^n
Sn=3+2*3^2+…+n3^n ①
①*3:3Sn=3^2+2*3^3+…+(n-1)3^n+n3^(n+1) ②
②-①:2Sn=n3^(n+1)-(3+3^2+…+3^n)=n3^(n+1)-3(3^n-1)/2
Sn=n3^(n+1)/2-3^(n+1)/4+3/4.
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