Mathegoras

Sequences and series › Infinite series › Alternating fraction sums

Nested half-fraction sum

High school · ●●●○○ 50 pts

Find the value of 2002+12(2001+12(2000+⋯+12(3+12⋅2))⋯ )2002 + \frac{1}{2} \left( 2001 + \frac{1}{2} \left( 2000 + \dots + \frac{1}{2} \left( 3 + \frac{1}{2} \cdot 2 \right) \right) \dotsb \right).

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geometric seriesseries manipulationtelescoping sums