(2n-1)×2的(2n-2)次方 求其n项和

Sn=1+3*2^2+5*2^4+...+(2n-1)×2^(2n-2)
4Sn=2^2+3*2^4+5*2^6+...+(2n-1)*2^2n
Sn-4Sn=1+2*2^2+2*2^4+...+2*2^(2n-2)-(2n-1)*2^2n
=1+[2^3+2^5+...+2^(2n-1)] -(2n-1)*2^2n
=1+2^3*(4^(n-1)-1)/(4-1)-(2n-1)*2^2n
=2/3+2*2^2n/3-(2n-1)*2^2n
=2/3-(2n-5/3)*2^2n

-3Sn=2/3-(2n-5/3)*2^2n
Sn=(2n/3-5/9)*2^2n-2/9

由题意得：
Sn=1*2^0+3*2^2+5*2^4+…………+(2n-1)2^(2n-2) (1)式
(2^2)Sn=1*2^2+3*2^4+5*2^6+………+(2n-3)2^(2n-2)+(2n-1)2^(2n) （2）式
由（1）-（2）得：
（1-4）Sn=1*2^0+2[2^2+2^4+2^6+………+2^(2n-2)]+(2n-1)2^(2n)
Sn=[(2n-1)/3]2^(2n)-1/9[4^(n+1)-1]

Sn=1+3*2^2+5*2^4+...+(2n-1)×2^(2n-2)
4Sn=2^2+3*2^4+5*2^6+...+(2n-1)*2^2n
Sn-4Sn=1+2*2^2+2*2^4+...+2*2^(2n-2)-(2n-1)*2^2n
=1+[2^3+2^5+...+2^(2n-1)] -(2n-1)*2^2n
=1+2^3*(4^(n-1)-1)/(4-1)-(2n-1)*2^2n
=2/3+2*2^2n/3-(2n-1)*2^2n
=2/3-(2n-5/3)*2^2n
-3Sn=2/3-(2n-5/3)*2^2n
Sn=(2n/3-5/9)*2^2n-2/9