The proof of an equivalence of D’alembert’s and Cauchy’s tests in the theory of numerical series
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...
Збережено в:
| Дата: | 2013 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут проблем штучного інтелекту МОН України та НАН України
2013
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| Назва видання: | Искусственный интеллект |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/85175 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 to formulate a new test of the
convergence for series with positive terms. The test is equivalent to Dalembert and Cauchy’s radical tests, but
it has some advantages. It can be applied to any series within Cauchy-D’alembert’s theory. |
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