(1)
a1=S1=1-a1
2a1=1
a1=1/2
Sn=1-an
Sn-1=1-a(n-1)
an=Sn-Sn-1=a(n-1)-an
2an=a(n-1)
an/a(n-1)=1/2,為定值.
數(shù)列{an}是首項(xiàng)為1/2,公比為1/2的等比數(shù)列.
an的通項(xiàng)公式為an=1/2^n
(2)
bn=n/an=n/2^n
Tn=1/2^1+2/2^2+3/2^3+...+n/2^n
(1/2)Tn=1/2^2+2/2^3+(n-1)/2^n+n/2^(n+1)
(1/2)Tn=Tn-(1/2)Tn=1/2^1+1/2^2+...+1/2^n-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-(n+2)/2^(n+1)
Tn=2-(n+2)/2^n