Question

Find the Maclaurin series for f(x) = (5x)/((x^2)-2x-24) and determine the radius of convergence.

Answer 1

Have you considered a partial fraction decomposition?

Answer 2

Kind of, but I'm not sure how to break it up

Answer 3

so I got 2/x+4 + 3/x-6

Answer 4

Well, you should remember your Order of Operations and add parentheses where necessary to mean what you intend. These are now trivial by themselves.

\(\dfrac{2}{4+x} = \dfrac{1/2}{1+(x/4)} = \dfrac{1/2}{1-(-x/4)} = \dfrac{1}{2}\left(1 + \left(\dfrac{-x}{4}\right)+ \left(\dfrac{-x}{4}\right)^{2} + \;etc.\right)\)

Okay, now you do the other one.