In each of the following, the function f(x) is the generating function for the sequence a0, a1,

Question:

In each of the following, the function f(x) is the generating function for the sequence a0, a1, a2, ..., whereas the sequence b0, b1, b2, ....... is generated by the function g(x). Express g(x) in terms of f(x).
(a) b3 = 3
bn = an, n ∈ N, n ≠ 3
(b) b3 = 3
b7 = l
bn = an, n ∈ N, n ≠ 3, 7
(c) b1 = 1
b3 = 3
bn = 2an, n ∈ N, n ≠ 1, 3
d) b1 = 1
b3 = 3
b7 = l
bn = 2an + 5, n ∈ N, n ≠ 1, 3, 7