Related:
Absolute convergence,
Cauchy,
Comparison test,
Complex number,
Convergence test,
Convergence tests,
Convergent series,
Corollary,
Geometric series,
Infinite series,
International Standard Book Number,
Limit superior,
Mathematics,
Natural number,
PlanetMath,
Power series,
Ratio test,
In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series
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.
Augustin-Louis Cauchy (21 August 1789 – 23 May 1857; French pronunciation: [oɡystɛ̃ lwi koˈʃi]) was a French mathematician who was an early pioneer of analysis. He started the project of formulating and proving the theorems of infinitesimal calculus in a rigorous manner. He also gave several important theorems in complex analysis and initiated the study of permutation groups in abstract algebra. A profound mathematician, Cauchy exercised a great influence over his contemporaries and successors. His writings cover the entire range of mathematics and mathematical physics.
In mathematics, the comparison test, sometimes called the direct comparison test or CQT is a criterion for convergence or divergence of a series whose terms are real or complex numbers. The test determines convergence by comparing the terms of the series in question with those of a series whose convergence properties are known.A complex number, in mathematics, is a number comprising a real number and an imaginary number. It can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit with the property i 2 = −1.[1] The complex numbers contain the ordinary real numbers, but extend them by adding in extra numbers and correspondingly expanding the understanding of addition and multiplication. This is in order to form a closed field, where any polynomial equation has a root, including examples such as x2 = −1.
In mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series.