Question

find a power series representation for the function
f(x)=(4+x)/(1-x)

Answer 1

\[f(x)=4+5\sum_{n=1}^{\infty} \] this is also part of the problem

Answer 2

One way is to know the power series for 1/(1-x) = 1+x+x^2+x^3...
and then get a new one by multiplying term by term with (4+x).

Alternatively, use Taylor expansion formula with derivatives etc.

Answer 3

i haven't learned the taylor series yet

Answer 4

Fine. Try my first approach?

Answer 5

can you give me an example to how to start it?