# Does it converge?

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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