(Ⅰ)数列{an}是公差为2的等差数列,a1+1,a3+1,a7+1成等比数列,a3=a1+5,a7=a1+13
所以由(a3+1)2=(a1+1)?(a7+1)…(3分)
得(a1+5)2=(a1+1)?(a1+13)
解之得a1=3,所以an=3+2(n-1),即an=2n+1…(6分)
(Ⅱ)由(1)得an=2n+1,
bn=
=1
an2?1
=1
(2n+1)2?1
?1 4
=1 n(n+1)
(1 4
?1 n
)…(9分)1 n+1
Tn=
(1?1 4
+1 2
?1 2
+…+1 3
?1 n
)=1 n+1
…(12分)n 4(n+1)