HMMT 2002 A10

Determine the value of

$2002+\frac{1}{2}\left(2001+\frac{1}{2}\left(2000+\cdots+\frac{1}{2}\left(3+\frac{1}{2} \cdot 2\right)\right) \cdots\right) .$

Dataset text NuminaMath olympiads. Quoted with source.

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4002

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