Millin Series

The series with sum

$$S'\equiv \sum_{n=0}^\infty {1\over F_{2^n}}={\textstyle{1\over 2}}(7-\sqrt{5}\,),$$

where $F_k$ is a Fibonacci Number (Honsberger 1985).

See also Fibonacci Number

References

Honsberger, R. Mathematical Gems III. Washington, DC: Math. Assoc. Amer., pp. 135-137, 1985.