An algebra problem by Julian Yu

Algebra Level 3

Suppose that x20172x+1=0{x}^{2017}-2x+1=0 for x1x\neq1. Find the value of 1+x+x2+x3++x20161+x+{x}^{2}+{x}^{3}+\cdots+{x}^{2016} .

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