Search results
Results From The WOW.Com Content Network
In mathematics, a series is the sum of the terms of an infinite sequence of numbers. More precisely, an infinite sequence defines a series S that is denoted. The n th partial sum Sn is the sum of the first n terms of the sequence; that is, A series is convergent (or converges) if and only if the sequence of its partial sums tends to a limit ...
The sum of the reciprocal of the primes increasing without bound. The x axis is in log scale, showing that the divergence is very slow. The red function is a lower bound that also diverges. The sum of the reciprocals of all prime numbers diverges; that is: This was proved by Leonhard Euler in 1737, [1] and strengthens Euclid 's 3rd-century-BC ...
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]
The Divergent Series is an American dystopian science fiction action film series based on the Divergent novels by the American author Veronica Roth. Distributed by Summit Entertainment and Lionsgate Films, the series set in a dystopian society: Divergent, Insurgent, and Allegiant. They have been produced by Lucy Fisher, Pouya Shabazian, and ...
In mathematics, the Riemann series theorem, also called the Riemann rearrangement theorem, named after 19th-century German mathematician Bernhard Riemann, says that if an infinite series of real numbers is conditionally convergent, then its terms can be arranged in a permutation so that the new series converges to an arbitrary real number, or ...
In geometrical optics, vergence describes the curvature of optical wavefronts. [1] Vergence is defined as. where n is the medium's refractive index and r is the distance from the point source to the wavefront. Vergence is measured in units of dioptres (D) which are equivalent to m −1. [1] This describes the vergence in terms of optical power.
N. H. Abel, letter to Holmboe, January 1826, reprinted in volume 2 of his collected papers. In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit. If a series converges, the individual terms of the series must approach zero. Thus any series in which the individual terms ...
Calculus. 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.