求Sn=2/2+3/2²+4/2³+……+(n/2ⁿ﹣¹)+(n+1/2ⁿ)

来源：学生作业学帮网编辑：学帮网时间：2024/05/13 13:14:27

Sn=2/2+3/2²+4/2³+……+(n/2ⁿ﹣¹)+(n+1/2ⁿ)
1/2Sn= 2/2²+3/2³+……+(n-1)/2ⁿ﹣¹+n/2ⁿ+(n+1)/2^(n+1)
Sn-1/2Sn=1+1/2^2+1/2^3+...+1/2^(n-1)+1/2^n+(n+1)/2^(n+1)
1/2Sn=1+(n+1)/2^(n+1)+(1/4)[1-1/2^(n-1)]/(1-1/2)
=1+(n+1)/2^(n+1)+1/2-1/2^n
=3/2+(n-1)/2^(n+1)

2*Sn=2+3/2+4/2²+5/2³+……+((n+1)/2ⁿ﹣¹)
Sn=2*Sn-Sn=2+(3/2-2/2)+(4/2²-3/2²)……