Convergence for Series With Terms Defined by a Recurrence Relation

被引：1
|
作者：
Easdale, Evelyn R. [1 ]
Fleming, Jolene E. [1 ]
Suceava, Bogdan D. [1 ]
机构：
[1] Calif State Univ Fullerton, Dept Math, McCarthy Hall 154, Fullerton, CA 92834 USA
来源：
AMERICAN MATHEMATICAL MONTHLY | 2017年 / 124卷 / 04期
关键词：
D O I：
10.4169/amer.math.monthly.124.4.360
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate whether a series Sigma(infinity)(n = 1) xn with terms defined recursively by the relation x(n+ 1) = f (x(n)), for all n = 1, converges or diverges. For the examples studied, the ratio test is inconclusive. We provide a theorem to decide whether such series are either convergent or divergent under some natural analytic conditions.
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页码：360 / 364
页数：5
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