Maclaurin Series Question

Question

Question: Find the Maclaurin series representation for f(x) = (1/(3-x))

Understanding:

I understand what to do until find the kth derivative, but am struggling to find a generalized formula.

How do you find a the Maclaurin representation for this question, and is there any technique on how to do so?

Answer 1

Divide 1 by (3-x) by long division and you should get

(1/3)[1+(x/3)+(x/3)²+(x/3)³+....]

This is the Maclaurin series for the function f(x) in your problem.

And it converges for |x|<1/3.

This is much easier than trying to get the derivatives directly.