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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.
First is the general direct comparison test: [51] [52] [47] For any series ... alternate in sign. Second is the general limit comparison test: [53] [54] If ...
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 , a way of deducing the convergence or divergence of an infinite series or an improper integral.
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.
Limit comparison test; N. Nth-term test; R. Ratio test; Root test; S. Stolz–Cesàro theorem; W. Weierstrass M-test This page was last edited on 3 November 2020, at ...
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.