Exercise 7.

Use multiplication to find the generating function for the sequence of partial sums of Fibonacci numbers, \(S_0, S_1, S_2, \ldots\) where \(S_0 = F_0\text{,}\) \(S_1 = F_0 + F_1\text{,}\) \(S_2 = F_0 + F_1 + F_2\text{,}\) \(S_3 = F_0 + F_1 + F_2 + F_3\) and so on.