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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]
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 Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test. [1]
The prism fusion range (PFR) or fusional vergence amplitude is a clinical eye test performed by orthoptists, optometrists, and ophthalmologists to assess motor fusion, specifically the extent to which a patient can maintain binocular single vision (BSV) in the presence of increasing vergence demands. Motor fusion is largely accounted to ...
The geometric series is an infinite series derived from a special type of sequence called a geometric progression, which is defined by just two parameters: the initial term and the common ratio . Finite geometric series have a third parameter, the final term's power.
The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval. For a strictly unimodal function with an extremum inside the interval, it will find that extremum, while for an interval containing multiple extrema (possibly including the interval boundaries), it will converge to one of them.
The top and bottom images produce a dent or projection depending on whether viewed with cross- () or wall- () eyed vergence. An autostereogram is a two-dimensional (2D) image that can create the optical illusion of a three-dimensional (3D) scene. Autostereograms use only one image to accomplish the effect while normal stereograms require two.
Integral test for convergence. The integral test applied to the harmonic series. Since the area under the curve y = 1/x for x ∈ [1, ∞) is infinite, the total area of the rectangles must be infinite as well. In mathematics, the integral test for convergence is a method used to test infinite series of monotonic terms for convergence.
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 who published it in his textbook Cours d'Analyse 1821. [1]