How do I write this sum in summation notation? $$\sum_{n=?}^\infty \left(\frac{x^n}{?}\right) = \frac{x^0}{1} + \frac{x^1}{x^2 -1}+\frac{x^2}{x^4 - x^2 +1}+\frac{x^3}{x^6 -x^4 + x^2 -1}+\frac{x^4}{x^8-x^6 +x^4 - x^2 +1}+\cdots$$
I am pretty sure I have the numerator of the summation, $x^n$ correct, but don't know how to write the denominator because of the alternating signs in each term. As for the starting point, $n=?$, I think its going to be either $0$ or $1$, depending on the denominator - I don't want to be kicked from this site by attempting to divide by $0$ .

HINT
The denominators in every term, except the first, are the alternating sums of even powers.
\begin{array}
.x^2-1 &\equiv& x^2 - x^0 \\
x^4-x^2+1 &\equiv& x^4 - x^2 + x^0 \\
x^6-x^4+x^2-1 &\equiv& x^6-x^4+x^2-x^0
\end{array}
Putting these in to summation notation:
\begin{array}
.x^2-x^0 &\equiv& \sum_{k=0}^1 (-1)^{k}x^{2(1-k)} \\ \\
x^4-x^2+x^0 &\equiv& \sum_{k=0}^2 (-1)^{k}x^{2(2-k)} \\ \\
x^6-x^4+x^2-x^0 &\equiv& \sum_{k=0}^3 (-1)^{k}x^{2(3-k)} \\ \\
\cdots\cdots\cdots &\equiv& \sum_{r=1}^n\sum_{k=0}^r(-1)^kx^{2(r-k)}
\end{array}
