Is here some way to expand a rational function to an infinite sum in Mathematica, i.e., a series? I want the general term of the series.
For example, $\dfrac{2}{3(x-1)^3}$
In Mathematica 10 you can use SeriesCoefficient
and Inactive
to get what you require
Inactive[Sum][SeriesCoefficient[2/(3(x-1)^3),{x,0,n},Assumptions->n>=0]x^n,{n,0,\[Infinity]}]
where Inactive
prevents Sum
from evaluating.
You can then "activate" the Sum
as follows
Activate[%]
to get back to your original expression.
Series
? $\endgroup$