Mathegoras

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Nested fraction sum with halving

High school · ●●○○○ 20 pts

Determine the value of 2002+12(2001+12(2000+⋯+12(3+12⋅2))⋯ )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).

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telescoping sumsgeometric series