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Abel's test

In mathematics, Abel's test (also known as Abel's criterion) is a method of testing for the convergence of an infinite series. The test is named after mathematician Niels Henrik Abel. There are two sl

Dini test

In mathematics, the Dini and Dini–Lipschitz tests are highly precise tests that can be used to prove that the Fourier series of a function converges at a given point. These tests are named after Uliss

Dirichlet's test

In mathematics, Dirichlet's test is a method of testing for the convergence of a series. It is named after its author Peter Gustav Lejeune Dirichlet, and was published posthumously in the Journal de M

Cauchy condensation test

In mathematics, the Cauchy condensation test, named after Augustin-Louis Cauchy, is a standard convergence test for infinite series. For a non-increasing sequence of non-negative real numbers, the ser

Limit comparison test

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.

Nth-term test

In mathematics, the nth-term test for divergence is a simple test for the divergence of an infinite series: If or if the limit does not exist, then diverges. Many authors do not name this test or give

Ratio test

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 an is nonzero when n is large. The test was first published by

Convergence tests

In mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series .

Alternating series test

In mathematical analysis, the alternating series test is the method used to show that an alternating series is convergent when its terms (1) decrease in absolute value, and (2) approach zero in the li

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 the con

Weierstrass M-test

In mathematics, the Weierstrass M-test is a test for determining whether an infinite series of functions converges uniformly and absolutely. It applies to series whose terms are bounded functions with

Root test

In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series. It depends on the quantity where are the terms of the series, and states that the series co

Cauchy's convergence test

The Cauchy convergence test is a method used to test infinite series for convergence. It relies on bounding sums of terms in the series. This convergence criterion is named after Augustin-Louis Cauchy

Integral test for convergence

In mathematics, the integral test for convergence is a method used to test infinite series of monotonous terms for convergence. It was developed by Colin Maclaurin and Augustin-Louis Cauchy and is som

Stolz–Cesàro theorem

In mathematics, the Stolz–Cesàro theorem is a criterion for proving the convergence of a sequence. The theorem is named after mathematicians Otto Stolz and Ernesto Cesàro, who stated and proved it for

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