Find a power series representation of the function:

$\displaystyle f(x) = \frac{2+x}{1-x}$

Here is what I did:

$\displaystyle f(x) = (2+x)(\frac{1}{1-x})$

$\displaystyle 2+x \sum^{\infty}_{n=0} (x)^n$

$\displaystyle = 2 + \sum^{\infty}_{n=0} x^{2n}$

Which is not right. The correct answer is:

$\displaystyle 2 + 3 \sum^{\infty}_{n=1}x^n$

But I don't understand how you would get that answer.