Hi,

I'm asked to represent $\displaystyle f(x) = \frac{1+x}{1-x}$ as a power series. Clearly it is similar to the geometric form $\displaystyle f(x) = \frac{1}{1-x}$.

I proceeded as follows: $\displaystyle f(x) = \frac{1+x}{1-x} = \frac{1}{1-x}+\frac{x}{1-x} = \Sigma x^n + \Sigma x^{n+1} = \Sigma x^n + x^{n+1}$.

Of course this isn't in the form of a power series, but I don't really know where to go from here. The answer according to my text is $\displaystyle 1 + 2\Sigma x^n$ - But I really don't know how they arrived at this - I tried to go backwards from the answer but ended up with something different from the original problem...so I don't know.

Thanks for the help ~ Might have a lot more questions on this topic hehe