Search results
Results from the WOW.Com Content Network
If r > 1, then the series diverges. If r = 1, the root test is inconclusive, and the series may converge or diverge. The root test is stronger than the ratio test: whenever the ratio test determines the convergence or divergence of an infinite series, the root test does too, but not conversely. [1]
With the series victory, India held all the series titles against all of the other Test sides at the same time. [5] The Board of Control for Cricket in India (BCCI) confirmed the dates of the tour in October 2016. [6] DRS was used for the first time in the Border–Gavaskar Trophy in this series, [7] although Hot Spot was not used. [8]
The Australia national cricket team toured India in the 2004–05 season and played a four-match Test series, during October and November 2004, against India, Australia winning the series 2–1 with one match drawn, their first series win on Indian soil since their 1969–70 tour.
Below is a summary of all Test series played prior to the Benaud–Qadir Trophy between Australia and Pakistan from 1956 to 2019, covering a 63-year period. [10] Australia and Pakistan competed against each other in 25 Test series, with Australia winning 13, Pakistan winning seven, and five Test series ending in a draw.
In mathematics, the Weierstrass M-test is a test for determining whether an infinite series of functions converges uniformly and absolutely.It applies to series whose terms are bounded functions with real or complex values, and is analogous to the comparison test for determining the convergence of series of real or complex numbers.
In mathematical analysis, the alternating series test is the method used to show that an alternating series is convergent when its terms (1) decrease in absolute value, and (2) approach zero in the limit. The test was used by Gottfried Leibniz and is sometimes known as Leibniz's test, Leibniz's rule, or the Leibniz criterion. The test is only ...
In mathematics, Dirichlet's test is a method of testing for the convergence of a series that is especially useful for proving conditional convergence. It is named after its author Peter Gustav Lejeune Dirichlet , and was published posthumously in the Journal de Mathématiques Pures et Appliquées in 1862.
Abel's uniform convergence test is a criterion for the uniform convergence of a series of functions or an improper integration of functions dependent on parameters. It is related to Abel's test for the convergence of an ordinary series of real numbers, and the proof relies on the same technique of summation by parts. The test is as follows.