数列 an=2n-1 设bn=an/3^n 求和tn=b1+..bn?

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/09 05:44:33

Tn=1/3+3/9+5/27+.+(2n-1)/3^n -----------(1)
(1)×1/3
1/3Tn=1/9+3/27+5/81+.+(2n-3)/3^n+(2n-1)/3^(n+1) ----(2)
(1)-(2):
2/3Tn=1/3+2/9+2/27+.+2/3^n-(2n-1)/3^(n+1)
=1/3+2/9[1-1/3^(n-1)]/(1-1/3)-(2n-1)/3^(n+1)
=1/3+1/3-1/3^n-(2n-1)/3^(n+1)
=2/3-(2n+2)/3^(n+1)
∴ Tn=1-(n+1)/3^n

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