a) Find a power series for f'(x) by starting with the convergent geometric series
b) Find a power series of f(x) and it's radius of convergence.
Do you understand what the question is asking you to do? You know that (note the "3", not "2", in the numerator. I assume that was a typo). You should also know that a "geometric series" is a series of the form and that the sum of such a series is as long as |r|< 1 so that the series converges.
Now look at . That is not quite in the form but can be put in that form. Divide both numerator and denominator by 27 and you get . Now do you see what "a" and "r" must be?