(b) Suppose G(r) is the generating function of a sequence (an)o, satisfying G'(r) =rG(r), G(0) = 1. i. Use the ODE to show that G'(0) = 0 and use this information, together with G(0) 1, to find ao and a₁. ii. Show that the sequence satisfies the recursive formula an = an-2. n iii. Show that an = 0 for n odd and find explicitly a2 and a4.
