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  2. Convergence tests - Wikipedia

    en.wikipedia.org/wiki/Convergence_tests

    The test is inconclusive if the limit of the summand is zero. This is also known as the nth-term test , test for divergence , or the divergence test . Ratio test

  3. nth-term test - Wikipedia

    en.wikipedia.org/wiki/Nth-term_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.

  4. Ratio test - Wikipedia

    en.wikipedia.org/wiki/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 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.

  5. Limit comparison test - Wikipedia

    en.wikipedia.org/wiki/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. Statement [ edit ]

  6. Summation - Wikipedia

    en.wikipedia.org/wiki/Summation

    In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.

  7. Dirichlet's test - Wikipedia

    en.wikipedia.org/wiki/Dirichlet's_test

    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.

  8. Abel's test - Wikipedia

    en.wikipedia.org/wiki/Abel's_test

    Abel's uniform convergence test is a criterion for the uniform convergence of a series of functions or an improper integration of functions dependent on parameters. It is related to Abel's test for the convergence of an ordinary series of real numbers, and the proof relies on the same technique of summation by parts. The test is as follows.

  9. Lebesgue integral - Wikipedia

    en.wikipedia.org/wiki/Lebesgue_integral

    Summand limit (term test) Ratio; ... the Lebesgue definition makes it possible to calculate integrals for a broader class of functions. ... The value of a measure at ...