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A note on Cauchy's root test

Published online by Cambridge University Press:  18 May 2009

I. S. Murphy
I. S. Murphy
Affiliation:
University of Glasgow, Scotland
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Throughout this note we deal with a series Σan of positive terms. The following tests for the convergence of this series are well-known.

Test 1. (Ratio test). LetThen, if K < 1, Σanconverges, while if K > 1, Σandiverges.

Test 2. (Root test). LetThen, if K < 1, Σanconverges, while if K > 1, Σandiverges.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 17 , Issue 2 , July 1976 , pp. 151 - 154
Copyright
Copyright © Glasgow Mathematical Journal Trust 1976

References

REFERENCES

1.Bromwich, T. J. I'A., Infinite series (Macmillan, 1908).Google Scholar
2.Knopp, K., Theory and application of infinite series (Blackie, 1928).Google Scholar
3.Phillips, E. G., A course of analysis (Cambridge, 1962).Google Scholar
4.Rankin, R. A., An introduction to mathematical analysis (Pergamon, 1963).Google Scholar