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

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

Let an =ƒ(n)/g(n) whereƒ and g are polynomials of degrees r and s respectively, and r < s so that limn->oo an = 0. The traditional method in determining convergence or divergence of an infinite series of the form En 00=1 an uses the limit-comparison test where the general term an of the given...

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Main Author: Lawas, Cresencia M.
Format: text
Published: Animo Repository 2003
Subjects:
Series, Infinite
Convergence
Divergent series
Mathematics
Online Access:https://animorepository.dlsu.edu.ph/faculty_research/7733
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Institution: De La Salle University
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spelling oai:animorepository.dlsu.edu.ph:faculty_research-82442022-11-19T00:02:00Z A generalization of the p-series test in determining convergence or divergence of an infinite series Lawas, Cresencia M. Let an =ƒ(n)/g(n) whereƒ and g are polynomials of degrees r and s respectively, and r < s so that limn->oo an = 0. The traditional method in determining convergence or divergence of an infinite series of the form En 00=1 an uses the limit-comparison test where the general term an 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 En 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. 2003-05-01T07:00:00Z text https://animorepository.dlsu.edu.ph/faculty_research/7733 Faculty Research Work Animo Repository Series, Infinite Convergence Divergent series Mathematics
institution De La Salle University
building De La Salle University Library
continent Asia
country Philippines
Philippines
content_provider De La Salle University Library
collection DLSU Institutional Repository
topic Series, Infinite
Convergence
Divergent series
Mathematics
spellingShingle Series, Infinite
Convergence
Divergent series
Mathematics
Lawas, Cresencia M.
A generalization of the p-series test in determining convergence or divergence of an infinite series
description Let an =ƒ(n)/g(n) whereƒ and g are polynomials of degrees r and s respectively, and r < s so that limn->oo an = 0. The traditional method in determining convergence or divergence of an infinite series of the form En 00=1 an uses the limit-comparison test where the general term an 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 En 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.
format text
author Lawas, Cresencia M.
author_facet Lawas, Cresencia M.
author_sort Lawas, Cresencia M.
title A generalization of the p-series test in determining convergence or divergence of an infinite series
title_short A generalization of the p-series test in determining convergence or divergence of an infinite series
title_full A generalization of the p-series test in determining convergence or divergence of an infinite series
title_fullStr A generalization of the p-series test in determining convergence or divergence of an infinite series
title_full_unstemmed A generalization of the p-series test in determining convergence or divergence of an infinite series
title_sort generalization of the p-series test in determining convergence or divergence of an infinite series
publisher Animo Repository
publishDate 2003
url https://animorepository.dlsu.edu.ph/faculty_research/7733
_version_ 1767196719054848000

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