A GENERALIZATION OF BERTRAND'S TEST

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TABATABAI ADNANI A.A.; REZA A.; MOROVATI M.

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ISSN: 2588-4824

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Paper Information

Journal: Journal of Linear and Topological Algebra Year:2013 | Volume:2 | Issue:3 Page(s): 141-147

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Title

A GENERALIZATION OF BERTRAND'S TEST

Author(s)

TABATABAI ADNANI A.A. | REZA A. | MOROVATI M. | Issue Writer Certificate

Keywords

BERTRAND'S TEST

CONVERGENCE TEST

SERIES TEST

Abstract

One of the most practical routine tests for convergence of a positive series makes use of the ratio test. If this test fails, we can use Rabbe's test. When Rabbe's test fails the next sharper criteria which may sometimes be used is the BERTRAND'S TEST. If this test fails, we can use a generalization of BERTRAND'S TEST and such tests can be continued in finitely. For simplicity, we call ratio test, Rabbe's test, BERTRAND'S TEST as the BERTRAND'S TEST of order 0, 1 and 2, respectively. In this paper, we generalize BERTRAND'S TEST in order k for natural k>2.It is also shown that for any k, there exists a series such that the BERTRAND'S TEST of order fails, but such test of order k+1 is useful, furthermore we show that there exists a series such that for any k, BERTRAND'S TEST of order k fails. The only prerequisite for reading this article is a standard knowledge of advanced calculus.

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APA: Copy

TABATABAI ADNANI, A.A., REZA, A., & MOROVATI, M.. (2013). A GENERALIZATION OF BERTRAND'S TEST. JOURNAL OF LINEAR AND TOPOLOGICAL ALGEBRA, 2(3), 141-147. SID. https://sid.ir/paper/335584/en

Vancouver: Copy

TABATABAI ADNANI A.A., REZA A., MOROVATI M.. A GENERALIZATION OF BERTRAND'S TEST. JOURNAL OF LINEAR AND TOPOLOGICAL ALGEBRA[Internet]. 2013;2(3):141-147. Available from: https://sid.ir/paper/335584/en

IEEE: Copy

A.A. TABATABAI ADNANI, A. REZA, and M. MOROVATI, “A GENERALIZATION OF BERTRAND'S TEST,” JOURNAL OF LINEAR AND TOPOLOGICAL ALGEBRA, vol. 2, no. 3, pp. 141–147, 2013, [Online]. Available: https://sid.ir/paper/335584/en

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