比较:Sn=1/2+2/4+3/8+4/16……+n/2的n次方（n是正整数）与2的大小

Sn=1/2+2/2^2+3/2^3+4/2^4……+n/2^n
(1/2)*Sn= 1/2^2+2/2^3+3/2^4……+(n-1)/2^n+n/2^(n+1)
联立二式，得(1/2)*Sn=1/2+1/2^2+1/2^3+……+1/2^n-n/2^(n+1)=1-1/2^n-n/2^(n+1)
Sn=2-1/2^(n-1)-n/2^n所以Sn

Sn

Sn

2大

Sn=1/2+2/2^2+3/2^3+4/2^4……+n/2^n
(1/2)*Sn= 1/2^2+2/2^3+3/2^4……+(n-1)/2^n+n/2^(n+1)
联立二式,得(1/2)*Sn=1/2+1/2^2+1/2^3+……+1/2^n-n/2^(n+1)=1-1/2^n-n/2^(n+1)
Sn=2-1/2^(n-1)-n/2^n

Sn=1/2+2/4+3/8+4/16……+n/2^n----------------------------1式
1/2Sn= 1/4+2/8+3/16……+(n-1)/2^n+n/2^(n+1)----------2式
1式-2式得：1/2Sn=1/2+1/4+1/8+1/16+...+1/2^n-n/2^(n+1)
所以1/2Sn=[1/2（1-1/2^n）]/(1-1/2)-n/2^(n+1)
1/2Sn=1-1/2^n-n/2^(n+1)
所以Sn=2-1/2^(n-1)-n/2^n则Sn