Reduced Fibonacci Series

Algebra Level 4

It is certain that the infinite sum of Fibonacci numbers is infinite. Consider this sum:

\[\sum _{ n=1 }^{ \infty }{ \frac { { F }_{ n } }{ { 2 }^{ n+1 } } } .\]

If \({F}_{1} = 1, {F}_{2} = 1, {F}_{3} = 2, ... etc\), what is the value of the above sum?

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