Identities for the String-Product of Strings on Geometric Sequences

TL;DR

This paper introduces a new general principle for identities involving the product of any number of terms in a geometric sequence, independent of position or common ratio, expanding understanding of geometric sequence properties.

Contribution

The paper presents a novel, position- and ratio-independent identity for the product of multiple terms in geometric sequences.

Findings

New identity for geometric sequence products

Applicable regardless of term position or ratio

Enhances mathematical understanding of geometric sequences

Abstract

Geometric sequences are found documented as early as 300BC in the text, Book IX of Elements written by Euclid of Alexandria. In this paper a new principle for identities involving the product of any k-number of terms of a geometric sequence is presented. The results of which are independent from a specific positional term or the common ratio.