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Algebra Level 4

Suppose \(S\) denotes sum to infinity and \(S_n\) denotes the sum of \(n\) terms of the series \[1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\cdots\] such that \(S-S_n<\dfrac{1}{1000}\), then what will be the least value of \(n\)?

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