Cauchy's test for convergence

См. также в других словарях:

• Integral test for convergence — In mathematics, the integral test for convergence is a method used to test infinite series of non negative terms for convergence. An early form of the test of convergence was developed in India by Madhava in the 14th century, and by his followers …   Wikipedia

• Cauchy's test — may refer to:* Cauchy s root test * Cauchy s condensation test * the integral test for convergence, sometimes known as the Maclaurin Cauchy test These topics are named after Augustin Louis Cauchy, a French mathematician.disambig …   Wikipedia

• Cauchy condensation test — In mathematics, the Cauchy condensation test is a standard convergence test for infinite series. For a positive monotone decreasing sequence f ( n ), the sum :sum {n=1}^{infty}f(n) converges if and only if the sum :sum {n=0}^{infty} 2^{n}f(2^{n}) …   Wikipedia

• Convergence tests — In mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series. Contents 1 List of tests 2 Comparison 3 Examples …   Wikipedia

• Cauchy's convergence test — The Cauchy convergence test is a method used to test infinite series for convergence. A series:sum {i=0}^infty a iis convergent if and only if for every varepsilon>0 there is a number N inmathbb{N} such that:|a {n+1}+a {n+2}+cdots+a {n+p}|0 there …   Wikipedia

• Term test — In mathematics, the nth term test for divergence[1] is a simple test for the divergence of an infinite series: If or if the limit does not exist, then diverges. Many authors do not name this test or give it a shorter name.[2] Cont …   Wikipedia

• Augustin Louis Cauchy — Infobox Scientist name = Augustin Louis Cauchy image width = 200px caption = Augustin Louis Cauchy birth date = birth date|1789|8|21|df=y birth place = Paris, France death date = death date and age|1857|5|23|1789|8|21|df=y death place = Sceaux,… …   Wikipedia

• Absolute convergence — In mathematics, a series (or sometimes also an integral) of numbers is said to converge absolutely if the sum (or integral) of the absolute value of the summand or integrand is finite. More precisely, a real or complex series is said to converge… …   Wikipedia

• Root test — In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series:sum {n=1}^infty a n.It is particularly useful in connection with power series. The testThe root test was developed first by Cauchy and so… …   Wikipedia

• Uniform convergence — In the mathematical field of analysis, uniform convergence is a type of convergence stronger than pointwise convergence. A sequence {fn} of functions converges uniformly to a limiting function f if the speed of convergence of fn(x) to f(x) does… …   Wikipedia

• Radius of convergence — In mathematics, the radius of convergence of a power series is a quantity, either a non negative real number or ∞, that represents a domain (within the radius) in which the series will converge. Within the radius of convergence, a power series… …   Wikipedia