Given the series:

a) find the radius of convergence (got that, it's z>1/3)

b) Prove that f is a rational function inside its circle of convergence

c) find the rational number f(2)

Well, I mess around with this for a while and get:

Which is interesting, and sort of reminds me of and , but a) I know multiplication of series doesn't work like that and b) that wouldn't be rational anyway. Any hints?