设数列{an}满足a1+3a2+3^2a3+.3^n-1×an=n/3,a∈N+.

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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.

$设数列{an}满足a1+3a2+3^2a3+.3^n-1×an=n/3,a∈N+.$

(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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