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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 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.
If p ≤ 0, then the nth-term test identifies the series as divergent. If 0 < p ≤ 1, then the n th-term test is inconclusive, but the series is divergent by the integral test for convergence . If 1 < p , then the n th-term test is inconclusive, but the series is convergent by the integral test for convergence.
While most of the tests deal with the convergence of infinite series, they can also be used to show the convergence or divergence of infinite products. This can be achieved using following theorem: Let { a n } n = 1 ∞ {\displaystyle \left\{a_{n}\right\}_{n=1}^{\infty }} be a sequence of positive numbers.
Divergent series (2 C, 15 P) L. Limits (mathematics) (1 C, 18 P) Pages in category "Convergence (mathematics)" ... Convergence problem; Convergent series;
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 series = converges if and only if the "condensed" series = converges.
Convergent thinking is a term coined by Joy Paul Guilford as the opposite of divergent thinking. It generally means the ability to give the "correct" answer to questions that do not require novel ideas, for instance on standardized multiple-choice tests for intelligence .
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 real or complex values, and is analogous to the comparison test for determining the convergence of series of real or complex numbers.