(1)解关于Sn的一元二次方程可得:
Sn=-1(舍去)或Sn=n^2+n
n>=2,an=Sn-S(n-1)=2n
a1=1+1=2
综上an=2n
(2)
bn
=(n+1)/[(n+2)²×4n² ]
=(4n+4)/[16(n+2)²×n² ]
=[1/n²-1/(n+2)²]/16
∴Tn
=[1/1²-1/3²+1/2²-1/4²+1/3²-1/5²+----1/(n-1)²-1/(n+1)²+1/n²-1/(n+2)²]/16
=[1/1²+1/2²-1/(n+1)²-1/(n+2)²]/16