Sn=n-5an-85 (1)
S（n+1）=n+1-5a（n+1）-85 (2)
(2)-(1)整理得6a(n+1)=1+5an
即a(n+1)-1=(5/6)(an-1)
又由S1=a1=1-5a1-85得a1=-14
所以{an-1}為首項-15,公比5/6的等比數(shù)列
所以an=(-15)*（5/6）^(n-1)+1
(2)bn=log5/6(5/6*(5/6)^0)+log5/6(5/6*(5/6)^1)+log5/6(5/6*(5/6)^2)+...+log5/6(5/6*(5/6)^(n-1))
=1+0+1+1+1+2+1+3+...+1+(n-1)
=n+(0+n-1)*n/2
=n(2+n-1)/2
=n(n+1)/2
1/bn=2/(n(n+1))=2[1/n-1/(n+1)]
Tn=2[1-1/2+1/2-1/3+,.+1/n-1/(n+1)]
=2[1-1/(n+1)]
=2n/(n+1)