What is the sum of power series (n-1) x ^ n and function?

Let f (x) = ∑ (n-1) x ^ n = x ^ 2 ∑ (n-1) x ^ (n-2). For G (x) = ∑ (n-1) x ^ (n-2), the integral term by term is as follows:
Σx^(n-1)=1/(1-x),|x|

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