Taylor Series of Rational Function

Question

I must admit that my understanding of Taylor and power series is flimsy at best. I am supposed to find the Taylor series for the following function centred at $x=0$:

$$\frac{1}{(1-5x)^2}$$

I honestly have no idea as to the approach to take from here. Should I look to relate this to the function $\frac{1}{1-x}$, attempt to determine the first few terms of the series and notice a pattern, or something else entirely? I'm not necessarily looking for an answer but rather an explanation as to how to best tackle problems of this nature.

Answer 1

HINT:

Let $f(x)=\frac{1/5}{1-5x}$ so that $f'(x)=\frac{1}{(1-5x)^2}$. Now, differentiate the geometric series for $f(x)$ term by term.