1)
A(n) = S(n) - S(n-1) (n≥2）
= n^2 - (n-1)^2
= 2n - 1
当n = 1时,A(1) = S(1) = 1
所以: A(n) = 2n - 1 (n∈N*)
2)
T(n) = b(1) + b(2) + …… + b(n)
= (1/2) + (1/2)^3 + (1/2)^5 + …… + (1/2)^(2n-1)
= (1/2)[ 1 - (1/4)^n ]/( 1 - 1/4 )
=2/3 - （2/3）*(1/4)^n
T(n) = 2/3 - （2/3）*(1/4)^n(n∈N*)