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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. ... Euler's formula; Partial fractions ... A commonly-used corollary of the integral test is the p-series test.
Second is the general limit comparison test: ... using comparisons to series representations of integrals ... form for the remainder of the Maclaurin formula. The ...
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.
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.
In mathematics, the integral test for convergence is a method used to test infinite series of monotonic terms for convergence. It was developed by Colin Maclaurin and Augustin-Louis Cauchy and is sometimes known as the Maclaurin–Cauchy test .
The root test is therefore more generally applicable, but as a practical matter the limit is often difficult to compute for commonly seen types of series. Integral test. The series can be compared to an integral to establish convergence or divergence. Let () = be a positive and monotonically decreasing function. If
In mathematics, comparison theorems are theorems whose statement involves comparisons between various mathematical objects of the same type, and often occur in fields such as calculus, differential equations and Riemannian geometry.