Sn=A1+A2+A3+……+An
=1/2+2/4+3/8+……+n/2^n
2Sn=1/1+2/2+3/4+……+n/2^(n-1)
两式错位相减
2Sn-Sn=1+[(2/2-1/2)+(3/4-2/4)+……+n/2^(n-1)-(n-1)/2^(n-1)]-n/2^n
=1+(1/2+1/4+……+1/2^(n-1))-n/2^n
=1×(1-1/2^n)/(1-1/2)-n/2^n
=2-(n+2)/2^n
Sn=A1+A2+A3+……+An
=1/2+2/4+3/8+……+n/2^n
2Sn=1/1+2/2+3/4+……+n/2^(n-1)
两式错位相减
2Sn-Sn=1+[(2/2-1/2)+(3/4-2/4)+……+n/2^(n-1)-(n-1)/2^(n-1)]-n/2^n
=1+(1/2+1/4+……+1/2^(n-1))-n/2^n
=1×(1-1/2^n)/(1-1/2)-n/2^n
=2-(n+2)/2^n