Exercise 3 Let P(2) and Q(2) be generating functions coding the sequences (Po, P1, p2, . ..) and (go, 91, 92, . . .), respectively, namely P(2) = >kxo Peak and Q(2) = >k20 9k2k. We want to understand how pretty standard mathematical operations on these generating func- tions corresponds to related operations on the sequences that they code. Most of the following are fairly straightorward to sort out. .. (a) Write the initial terms (coefficients) in the sequence coded by P(2) + Q(2). What does addition of two generating functions do to the sequences coded by these functions? (b) Write the initial terms in the sequence coded by 2P(2). What does multiplication by z do to the sequence coded by P(2)