## What is an Engel Expansion?

It turns out that each positive real number \(x\in\mathbb{R}^+\) can be written in the form \(x=1/a_1+1/a_1a_2+1/a_1a_2a_3+\cdots\), where \({a_1,a_2,a_3,\ldots}\) is a unique non-decreasing sequence, finite or infinite, of postive integers. This is called the *Engel expansion* of \(x\), after…