Let f(x) = t = 0 a1x1 with f(1) = t=0, a1 a finite number. Verfiy that

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Let f(x) =
∑∞t = 0 a1x1 with f(1) = ∑∞t=0, a1 a finite number. Verfiy that the quotient [f(x) - f(1)]/(x-1) is the generating function for the sequence s0,s1,s2......., where sn = ∑∞t= n+1 at , n ∈ N.
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