How would I find the closed form for the $n^{th}$ term of a sequence? Is there a general formula I can follow for these types of problems? Taking this sequence for example...
$$\frac{x^5}{(1-x)^4}$$
2026-03-28 00:26:24.1774657584
Closed form for nth term of generating function
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You divide out by the $x^{5}$ term, and so the coefficient of $x^{n}$ on the function you provided is the same as the coefficient of $x^{n-5}$ on $\dfrac{1}{(1-x)^{4}}$.
And so $\dfrac{1}{(1-x)^{4}} = \sum_{i=0}^{\infty} \binom{4 + i - 1}{i} x^{i}$.
So the coefficient of $x^{n}$ is $\binom{4 + n - 6}{n-5}$.