Relationship between root test and ratio for series

real analysis - relations between the root test and the ratio test - Mathematics Stack Exchange

relationship between root test and ratio for series

The test for whether a series is absolutely convergent by testing the limit of the absolute value of the ratio of successive terms of the series is called the ratio test. >If {a_n} is a sequence of complex numbers such that > >|a_n+1|/|a_n| = L (limit as n goes to infinity) > >then |a_n|^(1/n) = L (limit as n goes to infinity). The Root Test, like the Ratio Test, is a test to determine absolute convergence (or not). While the Solution: We run through our tests: Is this a geometric series?.

relationship between root test and ratio for series

Происходит восстановление! - кричал Джабба. - Все становится на свои места.

relationship between root test and ratio for series

Какой-то миг еще ощущались сомнения, казалось, что в любую секунду все снова начнет разваливаться на части. Но затем стала подниматься вторая стена, за ней третья. Еще несколько мгновений, и весь набор фильтров был восстановлен.

relationship between root test and ratio for series