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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.
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.
The cover of a test booklet for Raven's Standard Progressive Matrices. Raven's Progressive Matrices (often referred to simply as Raven's Matrices) or RPM is a non-verbal test typically used to measure general human intelligence and abstract reasoning and is regarded as a non-verbal estimate of fluid intelligence. [1]
Once this is done, the images around the matched patterns quickly become clear as the brain matches additional patterns using roughly the same degree of convergence. A type of wallpaper autostereogram featuring 3D objects instead of flat patterns ( ) The bottom part of this autostereogram is free of 3D images.
Picture arrangement test is a test that consists of a series of comic-strip-like pictures that are presented in a random order. The subject is given the task to arrange the pictures as quickly as possible so that a reasonable and meaningful story is formed. This is an example of a common feature found in intelligence tests. [1]
For example, in order to test the convergent validity of a measure of self-esteem, a researcher may want to show that measures of similar constructs, such as self-worth, confidence, social skills, and self-appraisal are also related to self-esteem, whereas non-overlapping factors, such as intelligence, should not relate.
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 .
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.