Abstract
This note considers some aspects of finite sums of unit fractions, including associated recurrence relations and conjectures in the context of experimental mathematics. Unit fractions provide a unifying theme.
Highlights
This paper considers conjectures in general and their mathematical context with particular applications to the Erdös-Straus conjecture with unit fractions as the unifying theme in the context of experimental mathematics
As an exercise in experimental mathematics [2], this note aims to elaborate some conjectures related to Egyptian fractions and harmonic numbers and to explore them with some recurrence relations and continued fractions
A further refinement of the work would be to investigate finite sums of reciprocals of distinct n primes [13], and we look at some other types of finite sums
Summary
As an exercise in experimental mathematics [2], this note aims to elaborate some conjectures related to Egyptian fractions and harmonic numbers and to explore them with some recurrence relations and continued fractions. In the context of teaching and learning in general they implicitly involve the relatively neglected educational concepts of functional literacy and numeracy [27]. Conjectures have an inherent fascination and challenge because we can neither prove them nor find counter examples [10] They can encourage non-standard mathematical skills such as shrewd guessing (or conjecturing) [21], considering integer structure [16], and new approaches to viewing the Cartesian plane [8] in the context of the history of mathematical conjectures [9]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
