1. Let f(x)=\frac{1}{(1-3 x)} \text { a) Determine the power series } \sum_{n=0}^{\infty} a_{n} x^{n} \text { of } f(x) \text {. } b) Calculate f' (x), the derivative of

f(x) with respect to x, and determine the power series of f'(x). How does this power series of f'(x) relate to the power series of f(x) found in part a)?