Sn=1/2+3/2^2+5/2^3+...+(2n-1)/2^n (1)
2Sn=2(1/2+3/2^2+5/2^3+...+(2n-1)/2^n)=1+3/2+5/2^2+...+(2n-1)/2^(n-1) (2)
两个式子相减(同分母的相减)
Sn=2Sn-Sn=1+2/2+2/2^2+...+2/2^(n-1)-(2n-1)/2^n
=2(1+1/2^2+1/2^3++...+2/2^(n-1)]-(2n-1)/2^n
=2(2-1/2^(n-1))-(2n-1)/2^n
Sn=1/2+3/2^2+5/2^3+...+(2n-1)/2^n (1)
2Sn=2(1/2+3/2^2+5/2^3+...+(2n-1)/2^n)=1+3/2+5/2^2+...+(2n-1)/2^(n-1) (2)
两个式子相减(同分母的相减)
Sn=2Sn-Sn=1+2/2+2/2^2+...+2/2^(n-1)-(2n-1)/2^n
=2(1+1/2^2+1/2^3++...+2/2^(n-1)]-(2n-1)/2^n
=2(2-1/2^(n-1))-(2n-1)/2^n