Does it converge?

Probability Level 3

Compute 12+14+28+316+532++Fk2k+ \frac{1}{2} + \frac{1}{4} + \frac{2}{8} + \frac{3}{16} + \frac{5}{32} + \dots + \frac{F_k}{2^k} + \dots where Fk F_k represents the the kth k^\text{th} term of the Fibonacci sequence: 1,1,2,3,5,8,13,...1, 1, 2, 3, 5, 8, 13, ...

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