how to find a power series centered at 0 for f(x)=((x^3)/((x-2)^2)?
The technique I used was just symbolic long division. You can look this up here:
The trick is to go BACKWARDS and not forwards.
Meaning first you divide x^3/4 and NOT x^3/x^2.
You’ll get a very long power series but it is not really predictable like e^x or another power series.
I’ll start it for you: