A generalization of the p-series test in determining convergence or divergence of an infinite series

Authors

Cresencia M. Lawas

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Conference Proceeding

Source Title

Mathematical Society of the Philippines. Annual Convention 2003

Publication Date

5-2003

Abstract

Let an =ƒ(n)/g(n) whereƒ and g are polynomials of degrees r and s respectively, and r < s so that lim_n->oo ^an = 0. The traditional method in determining convergence or divergence of an infinite series of the form E_n ⁰⁰=1 an uses the limit-comparison test where the general term a_n of the given series is compared with the general term of a known convergent or divergent p-series. In this paper. a much easier method called the polynomial test is presented. We also present a generalization of the polynomial test to deal with series of the form E_n ⁰⁰=1 where f and g are not polynomial functions of n. In this case, r and s would represent the highest exponents of n in f and g, respectively.

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Recommended Citation

Lawas, C. M. (2003). A generalization of the p-series test in determining convergence or divergence of an infinite series. Mathematical Society of the Philippines. Annual Convention 2003 Retrieved from https://animorepository.dlsu.edu.ph/faculty_research/7733

Disciplines

Mathematics

Note

Abstract only

Keywords

Series, Infinite; Convergence; Divergent series

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