1)a1=S1=1/2+3/2=2.
当n>=2时,an=Sn-S(n-1)=(1/2)n^2+(3/2)n-(1/2)(n-1)^2-(3/2)(n-1)=n+1,a1=2也适合此式.
所以,数列{an}的通项公式是an=n+1,n为正整数.
(2)数列{bn}的通项公式为：bn=1/[ana(n+1)]=1/[(n+1)(n+2)=1/(n+1)-1/(n+2),n为正整数.
(3)Tn=b1+b2+…+bn
=1/2-1/3+1/3-1/4+…+1/(n+1)-1/(n+2)
=1/2-1/(n+2)
=n/(2n+4)