已知数列{an}的通项公式an=2的n次方分之n,求Sn急要!

网友回答

a1=1/2
a2=2/2^2
a3=3/2^3
.an=n/2^n
Sn=1/2+2/2^2+3/2^3+.+n/2^n
1/2Sn=1/2^2+2/2^3+3/2^4+.+(n-1)/2^n+n/2^(n+1)
Sn-1/2Sn
=1/2+1/2^2+1/2^3+1/2^4+.1/2^2-n/2^(n+1)
=1/2*[1-(1/2)^n]/(1-1/2)-n/2^(n+1)
=1-(1/2)^n-n/2^(n+1)
=1-2^(-n)-n*(1/2)^(n+1)
=1-2^(-n)-n*2^(-n-1)
Sn=2*[1-2^(-n)-n*2^(-n-1)]
=2-2*2^(-n)-n*2^(-n)
=2-(n+2)*2^(-n)