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Some sequences by inverse iteration

Published online by Cambridge University Press:  01 August 2016

David Clegg  and
Victor Bryant
David Clegg
Affiliation:
Department of Mathematics, Statistics and Computing, Liverpool Polytechnic, Liverpool L3 3AF
Victor Bryant
Affiliation:
Department of Pure Mathematics, Sheffield University, Sheffield S3 7RH
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Extract

This article was inspired by the following problem in a recent addition of the Bulletin of the IMA:

Problem. The sequence a0, a1, a2, a3,… is defined by a0 = 3 and, for n ⩾ 1, an is the real root of the equation

Prove that the sequence converges to 5.

Type
Research Article
Information
The Mathematical Gazette , Volume 70 , Issue 454 , December 1986 , pp. 262 - 266
Copyright
Copyright © The Mathematical Association 1986

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