Ganita Bharati
Published in Association with Bulletin of The Indian Society for History of Mathematics
Current Volume: 45 (2023 )
ISSN: 0970-0307
Periodicity: Half-Yearly
Month(s) of Publication: June & December
Subject: Mathematics
DOI: https://doi.org/10.32381/GB
Online Access is Free for Life Member
Some Identities and Series Involving Arithmetic and Geometric Progressions in PÀÇÁgaõitam, GaõitasÀrasaôgrahaÍ and GaõitakaumudÁ
By : Shriram M. Chauthaiwale
Page No: 193-204
Abstract
The celebrity Indian mathematician trio ŒrÁdhara, MahÀvÁra and NÀrÀyaõa Paõçita elaborates on some identities which are either algebraic sums of numbers with the series on natural numbers or sums of series of natural numbers. Series involving arithmetic and geometric progressions are also found discussed. In this article we discuss these identities and the series, explaining the format of each one followed by their formulation. The rationale for the nontrivial results is provided. The results are amended and extended when necessary.