The proof of an equivalence of D’alembert’s and Cauchy’s tests in the theory of numerical series

• Published in: Искусственный интеллект
• Date: 2013
• Main Author: Mironenko, L.P.
• Format: Article
• Language: English
• Published: Інститут проблем штучного інтелекту МОН України та НАН України 2013
• Subjects: Обучающие и экспертные системы
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/85175
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The proof of an equivalence of D’alembert’s and Cauchy’s tests in the theory of numerical series / L.P. Mironenko // Искусственный интеллект. — 2013. — № 3. — С. 507–511. — Бібліогр.: 5 назв. — англ.

In the paper it is shown that D’alembert’s test and Cauchy’s radical test are not independent one from another. It is proposed a transition scheme from one test to another and vice versa. The equivalence of the tests is proved for series with the monotonically decreasing terms. This fact is used t...