Definition:Millin Series

Definition

The Millin series is the series defined as:

$\ds \sum_{n \mathop = 0}^\infty \frac 1 {F_{2^n} }$

where $F_k$ is the $k$th Fibonacci number.

Closed Form for Millin Series, where it is shown to evaluate to $\dfrac {7 - \sqrt 5} 2$

This entry was named for Dale A. Miller.

The series which is now known as the Millin series appeared as a puzzle problem in The Fibonacci Quarterly in $1974$ under the byline D.A. Millin, identified as a high school student in Pennsylvania, US.

Millin was in fact a misprint for D.A. Miller, under which name the solution was published.

An outline by Irving John Good of a solution appeared in the following issue.

A full solution by Anthony Greville Shannon was published two years later in The Fibonacci Quarterly, and in that issue, Miller's name was reported correctly as D. A. Miller.

The identity was published on the Mathworld website under the name Millin series, from which it has since been further propagated.

Weisstein, Eric W. "Millin Series." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MillinSeries.html