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$\large \sum^{\infty}_{n=1}{\dfrac{F_n}{2^n}}$

Find the sum above, where $F_n$ is the $n^{\text{th}}$ Fibonacci number that is $F_0 = 0$, $F_1 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 2$.

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