Article ID: MTJPAM-D-19-00008

Title: A SIMPLE PROOF OF A BINOMIAL IDENTITY WITH APPLICATIONS


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-19-00008; Volume 1 / Issue 2 / Year 2019, Pages 13-20

Document Type: Research Paper

Author(s): Ting-Ting Bai a , Qiu-Ming Luo b

aDepartment of Mathematics, Chongqing Normal University Chongqing Higher Education Mega Center, Huxi Campus Chongqing 401331, People’s Republic of China

bDepartment of Mathematics, Chongqing Normal University Chongqing Higher Education Mega Center, Huxi Campus Chongqing 401331, People’s Republic of China

Received: 5 December 2019, Accepted: 12 December 2019, Available online: 28 December 2019.

Corresponding Author: Qiu-Ming Luo (Email address: luomath2007@163.com)

Full Text: PDF

Abstract

Peterson [Amer. Math. Monthly, 120 (2013), 558–562] gave a probabilistic proof of a binomial identity. In this paper, by using the partial fraction decomposition, we give a simple proof of this binomial identity. As some applications, we obtain some interesting harmonic number identities.

Keywords: Binomial identity, Harmonic number, Bell polynomial, Partial fraction decomposition

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