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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]
Operation Castle was a United States series of high-yield (high-energy) nuclear tests by Joint Task Force 7 (JTF-7) at Bikini Atoll beginning in March 1954. It followed Operation Upshot–Knothole and preceded Operation Teapot .
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.
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.
Operation Upshot–Knothole was a series of eleven nuclear test shots conducted in 1953 at the Nevada Test Site.It followed Operation Ivy and preceded Operation Castle.. Over 21,000 soldiers took part in the ground exercise Desert Rock V in conjunction with the Upshot-Knothole Grable shot. [1]
Operation Roller Coaster [1] was a series of four nuclear tests conducted jointly by the United States and the United Kingdom in 1963, at the Nevada Test Site. [2] The tests did not involve the detonation of any nuclear weapons.
When the series is held in England, the England-India Test cricket series is played for the Pataudi Trophy. That trophy was instituted by the Marylebone Cricket Club (MCC) in 2007 to mark the 75th anniversary of the first England-India Test series held in England in 1932. [4] The trophy was named after the Pataudi cricketing family.
Greenwater, a Lawrence Livermore test, was to be fired in Area 19, [10] and was a test of an x-ray laser system. [12] The test was cancelled 16 July 1992. [13] The Greenwater nuclear device had already been assembled at the time of cancellation, and had to be dismantled. [14] A fourth test, Mighty Uncle, was planned for 1993.