This paper presents a new mathematical model for formation as well as computation of geometric series and summability in step-by-step procedures. Also, it provides mathematical structures for geometric series-ordered terms. The novel mathematical model uses Annamalai's computing method of geometric series and summability, which provided a technique to establish the algorithmic geometric series and its formulae in an earlier paper, for further improvement in the scientific research study. This mathematical/computational models of geometric series are widely used in the fields of physics, engineering, biology, medicine, economics, computer science, queueing theory, finance, and management for the purpose of research and development meeting today's challenges. In an earlier research article, the geometric series along with exponential decay model were used to determine effective medicine dosage. Few specific mathematical formulae had also been discovered by using Annamalai's algorithmic geometric series and summability. This could be very interesting and informative for current students and researchers.
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