# 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.

## Also see

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

## Source of Name

This entry was named for Dale A. Miller.

## Historical Note

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.

## Sources

- 1974: D.A. Millin:
*Advanced Problems and Solutions: H-237*(**Vol. 12**,*no. 3*: p. 309)

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