设数列An满足a1+3*a2+3^2*a3……+3^(n-1)*an=n/3,n属于正整数.求数列的{An}的通项公式.设bn=n/An,求是列{Bn}的前n和Sn

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设数列An满足a1+3*a2+3^2*a3……+3^(n-1)*an=n/3,n属于正整数.求数列的{An}的通项公式.设bn=n/An,求是列{Bn}的前n和Sn设数列An满足a1+3*a2+3^2

设数列An满足a1+3*a2+3^2*a3……+3^(n-1)*an=n/3,n属于正整数.求数列的{An}的通项公式.设bn=n/An,求是列{Bn}的前n和Sn
设数列An满足a1+3*a2+3^2*a3……+3^(n-1)*an=n/3,n属于正整数.
求数列的{An}的通项公式.
设bn=n/An,求是列{Bn}的前n和Sn

设数列An满足a1+3*a2+3^2*a3……+3^(n-1)*an=n/3,n属于正整数.求数列的{An}的通项公式.设bn=n/An,求是列{Bn}的前n和Sn
3^(n-1)*an=n/3-(n-1)/3=1/3(n>=2)
所以an=3^(-n)(n>=2)
带入n=1满足上式,所以an=3^(-n).
bn=n*3^n
Sn用错位相减求出,(写出Sn,乘3减Sn,等比求和)

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