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?
by
Steven Zheng