<s>[INST] Find the function that equals to $1-x^3+x^6-x^9+ \cdots$ 
Find the function that equals  to $1-x^3+x^6-x^9+ \cdots$ for all $|x| < 1$

I know that $\frac{1}{1+x} = 1-x+x^2-x^3+...$ But I couldn't find the pattern here
 [/INST] Hint: if $|f(x)| < 1$ then $$\frac{1}{1+f(x)} = 1 - f(x) + f(x)^2 - f(x)^3 + \dotsb$$
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