已知在数列{an}中,a1=1,当n≥2时,其前n项和Sn满足Sn2=an(Sn-
(Ⅰ) 求Sn的表达式; (Ⅱ) 设bn=
|
(Ⅰ)当n≥2时,an=Sn-Sn-1代入得:2SnSn-1+Sn-Sn-1=0⇔
-1 Sn
=2,1 Sn-1
∴
=2n-1⇔Sn=1 Sn
(6分)1 2n-1
(Ⅱ)bn=
=Sn 2n+1
=1 (2n-1)(2n+1)
(1 2
-1 2n-1
)1 2n+1
∴Tn=
[(1 2
-1 1
)+(1 3
-1 3
)+…+(1 5
-1 2n-1
)]=1 2n+1
.(13分)n 2n+1