求和Sn=1(1/3)+3(1/3)^2+5(1/3)^3+.+(2n-1)(1/3)^n

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/28 01:44:10

求和Sn=1*(1/3)+3*(1/3)^2+5*(1/3)^3+.+(2n-1)*(1/3)^n
求和Sn=1*(1/3) + 3*(1/3)^2 + 5*(1/3)^3 +.+(2n-1)*(1/3)^n

等差乘等比求和的思想是乘积求差法:
数列乘公比再与原数列求差
Sn=1*(1/3)+3*(1/3)^2+5*(1/3)^3+.+(2n-1)*(1/3)^n
那么(1/3)*Sn=1*(1/3)^2+3*(1/3)^3+5*(1/3)^3+.+(2n-1)*(1/3)^(n+1)
上减下得
(2/3)*Sn=2*(1/3)^2+2*(1/3)^3+...+2*(1/3)^n+1*(1/3)-(2n-1)*(1/3)^(n+1)
除开最后两项则前面为等差数列:
求和得1-(1/3)^(n-1)
所以(2/3)*Sn=1-(1/3)^(n-1)+1*(1/3)-(2n-1)*(1/3)^(n+1)
把2/3乘到右边
再自己化简吧.

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