设数列{An}满足 A1+3A2+3^2A3+……+3^n-1An=n/3 (n属于正整数) (1)求{An}的通项公式 (2)设Bn=n/An ,求{Bn}前n项和Sn.

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设数列{An}满足 A1+3A2+3^2A3+……+3^n-1An=n/3 (n属于正整数) (1)求{An}的通项公式 (2)设Bn=n/An ,求{Bn}前n项和Sn.
设数列{An}满足 A1+3A2+3^2A3+……+3^n-1An=n/3 (n属于正整数)
(1)求{An}的通项公式 (2)设Bn=n/An ,求{Bn}前n项和Sn.

设数列{An}满足 A1+3A2+3^2A3+……+3^n-1An=n/3 (n属于正整数) (1)求{An}的通项公式 (2)设Bn=n/An ,求{Bn}前n项和Sn.
(1)A1+3A2+3^2A3+……+3^n-1An=n/3
A1+3A2+3^2A3+……+3^n-1An+3^nAn+1=(n+1)/3
相减,3^nAn+1=1/3
所以,An+1=1/(3^n+1)
即An=1/3^n
(2)Bn=n/3^n
Sn是明显的差比数列,用错位相减

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