Subject generating function  Let a0 = 1 and an = 2an-1 + 1 for every n >1. Let G(x) be the generating function of the sequence a0,a1, a2,... Multiply both sides of an = 2an-1 + 1 by xn ,add those up from n = 1 to infinity. By using ∑ (n=0 to ∞) xn = 1/(1 - x) for |x| < 1, find a closed formula for G(x).

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.