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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.
Celebrate Recovery is one of the seven largest addiction recovery support group programs. [5] Promotional materials assert that over 5 million people have participated in a Celebrate Recovery step study in over 35,000 churches. [6] [7] Leaders seek to normalize substance abuse as similar to other personal problems common to all people. [8]
The test specifically measures a component of creativity called divergent thinking, which is the ability to find different solutions to open-ended problems. [ 4 ] There is an online version of the task [ 5 ] created by the authors who developed the DAT (Jay A. Olson, Johnny Nahas, Denis Chmoulevitch, Simon J. Cropper, Margaret E. Webb).
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 ]
If r < 1, then the series converges absolutely. If r > 1, then the series diverges. If r = 1, the root test is inconclusive, and the series may converge or diverge. The root test is stronger than the ratio test: whenever the ratio test determines the convergence or divergence of an infinite series, the root test does too, but not conversely. [1]
Many authors do not name this test or give it a shorter name. [2] When testing if a series converges or diverges, this test is often checked first due to its ease of use. In the case of p-adic analysis the term test is a necessary and sufficient condition for convergence due to the non-Archimedean ultrametric triangle inequality.
The process was adapted from the divergence-convergence model proposed in 1996 by Hungarian-American linguist Béla H. Bánáthy. [2] [3] The two diamonds represent a process of exploring an issue more widely or deeply (divergent thinking) and then taking focused action (convergent thinking). [4]
The only divergence for probabilities over a finite alphabet that is both an f-divergence and a Bregman divergence is the Kullback–Leibler divergence. [8] The squared Euclidean divergence is a Bregman divergence (corresponding to the function x 2 {\displaystyle x^{2}} ) but not an f -divergence.