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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. Statement [ edit ]
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. ... Examples. Consider the series
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.
Comparison test can mean: Limit comparison test, a method of testing for the convergence of an infinite series. Direct comparison 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.
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 test functions used to evaluate the algorithms for MOP were taken from Deb, [4] Binh et al. [5] and Binh. [6] The software developed by Deb can be downloaded, [ 7 ] which implements the NSGA-II procedure with GAs, or the program posted on Internet, [ 8 ] which implements the NSGA-II procedure with ES.