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In mathematics, the limit comparison test (LCT) (in contrast with the related direct comparison test) is a method of testing for the convergence of an infinite series.
1.6 Limit comparison test. 1.7 Cauchy condensation test. 1.8 Abel's test. 1.9 Absolute convergence test. 1.10 Alternating series test. 1.11 Dirichlet's test.
In mathematics, the comparison test, sometimes called the direct comparison test to distinguish it from similar related tests (especially the limit comparison test), provides a way of deducing whether an infinite series or an improper integral converges or diverges by comparing the series or integral to one whose convergence properties are known.
Comparison test can mean: Limit comparison test, a method of testing for the convergence of an infinite series. Direct comparison test, ...
In mathematics, the nth-term test for divergence [1] is a simple test for the divergence of an infinite series: If lim n → ∞ a n ≠ 0 {\displaystyle \lim _{n\to \infty }a_{n}\neq 0} or if the limit does not exist, then ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty }a_{n}} diverges.
The root test states that: if C < 1 then the series converges absolutely, if C > 1 then the series diverges, if C = 1 and the limit approaches strictly from above then the series diverges, otherwise the test is inconclusive (the series may diverge, converge absolutely or converge conditionally).
In mathematics, the ratio test is a test (or "criterion") for the convergence of a series =, where each term is a real or complex number and a n is nonzero when n is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test.
The departure of the upper tail of the distribution from the expected trend along the diagonal is due to the presence of substantially more large test statistic values than would be expected if all null hypotheses were true. The red point corresponds to the fourth largest observed test statistic, which is 3.13, versus an expected value of 2.06.