Reduced Fibonacci Series

Algebra Level 4

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

n=1Fn2n+1.\sum _{ n=1 }^{ \infty }{ \frac { { F }_{ n } }{ { 2 }^{ n+1 } } } .

If F1=1,F2=1,F3=2,...etc{F}_{1} = 1, {F}_{2} = 1, {F}_{3} = 2, ... etc, what is the value of the above sum?

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