<s>[INST] Series expansion of $\frac{1}{(1+x)(1−x)(1+x^2)(1−x^2)(1+x^3)(1−x^3)\cdots}$? How would I find the series expansion $\displaystyle\frac{1}{(1+x)(1−x)(1+x^2)(1−x^2)(1+x^3)(1−x^3)\cdots}$ so that it will turn into an infinite power series again?? 
 [/INST] $$\frac{1}{1-x^k}=1+x^k+x^{2k}+x^{3k}\cdots$$
$$\frac{1}{1+x^k}=1-x^k+x^{2k}-x^{3k}\cdots$$
</s>