Find a power series representation for (4+2x)/(1+x)

I know you have to do the power series for 1/(1+x) and then times it by (4+2x) but I don't know where to go from there.

Question

Find a power series representation for (4+2x)/(1+x)

I know you have to do the power series for 1/(1+x) and then times it by (4+2x) but I don't know where to go from there.

nottim · Answer

Argh. So difficult. show any work you did, to help someone else help you.

anonymous · Answer

Well it's just (4+2x)*power series ((-1)^n*(x)^n)

but the answer choices I have are just one power series (so no breaking the 4 and 2x up unless you combine power series), and some answer choices are 4 + power series

zarkon · Answer

$$\frac{4+2x}{1+x}=2+2\cdot\frac{1}{1+x}$$

anonymous · Answer

Wow I never would have seen that. Thank you so much.

zarkon · Answer

happy to help.