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.

引用

页码：360 / 364

页数：5

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