( Discrete Math )Please answer the questions in the attachment and providing working out on paper

Questions on 9.2 5. Let A(x) = 2x2 + 3x3 + 4x4 ... and B(x) = 1 -3x + 9x2 -27x3 + 81x4 + .... Calculate rational GFs for A(x), B(x), A(x) + B(x) and A'(x). 6. For the generating series B(x) in Q5, set on = [x"]B(x)2. Calculate a formula for cn. 7. Let an be the number of ways to select n balls from a large bag of red, blue, and yellow balls where the selection must include an even number of blue balls. Write down a generating func- tion for an in closed form