Thread: What happened to the x? f(x) to power series

Find a power series for the function:

f(x) = 1+x/1-x

so the solution shows:

f(x) = -1 + 2/1-x >>>>>>what happened to the +x in the numerator at this point?

-1+ 2 series sign x^n

When you do long division, the x gets divided by x somewhere, and x/x = 1

(1+x) / (1-x) gives -1, and a remainder of 2, hence,

$\displaystyle \dfrac{1+x}{1-x} = -1 + \dfrac{2}{1-x}$