Discrete maths. Finding generating sequence for function.

Question

I have a problem with generating sequences. I do not understand them at all. The task I have is:

Find generating sequence for f(x)=ln(1-x).

So, to my understanding, D(f)=(-infinity;0]

Edit: my domain ends at zero, because ln(0) has no meaning, but ln(1-0)=ln1=0.

Answer 1

A generating sequence $(a_n)_{n\ge 0}$ for a function $f(z)$ in a domain $D$ is a sequence such that $$ f(z) = \sum_{n \ge 0} a_n z^n $$ in the domain $D$.
Now, what do you know about the Taylor expansion of $f(z) = \ln (1-z)$ around $z=0$?