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Compute $\frac{1}{2} + \frac{1}{4} + \frac{2}{8} + \frac{3}{16} + \frac{5}{32} + \dots + \frac{F_k}{2^k} + \dots$ where $F_k$ represents the the $k^\text{th}$ term of the Fibonacci sequence: $1, 1, 2, 3, 5, 8, 13, ...$

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