On some properties of the alternating Sylvester series and alternating Engel series representation of real numbers

Abstract

We investigate some properties connected with the alternating Sylvester series and alternating Engel Series representation for real numbers, in terms of the integer digits involved. In particular, we look at an algorithm that leads to a general alternating series expansion for real numbers in terms of rationals and deduce the alternating Sylvester and alternating Engel series from this general series.

KEY WORDS: alternating Sylvester series, alternating Engel series, rational numbers, alternating series expansion.