What is the generating function for series with only one term missing?

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If I have a sequence $$1 + x^2 + x^3$$, what would the generating function for it be?

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Assuming that you're asking for $ 1 + x^2 + x^3 + x^4 + x^5 + \ldots $, then

Hint: The generating function for $ 1 + x + x^2 + \ldots $ is $\frac{1}{1-x}$.

Hence, the answer is

$ \frac{ 1}{1-x} - x$.