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Converging series

Converging Con*ver"ging, a. Tending to one point; approaching each other; convergent; as, converging lines. --Whewell. Converging rays(Opt.), rays of light, which, proceeding from different points of an object, tend toward a single point. Converging series (Math.), a series in which if an indefinitely great number of terms be taken, their sum will become indefinitely near in value to a fixed quantity, which is called the sum of the series; -- opposed to a diverging series.

Converging Con*ver"ging, a. Tending to one point; approaching each other; convergent; as, converging lines. --Whewell. Converging rays(Opt.), rays of light, which, proceeding from different points of an object, tend toward a single point. Converging series (Math.), a series in which if an indefinitely great number of terms be taken, their sum will become indefinitely near in value to a fixed quantity, which is called the sum of the series; -- opposed to a diverging series.

- series of f {\displaystyle f} converges uniformly, but not necessarily absolutely, to f {\displaystyle f} . A function ƒ has an absolutely converging...

- generally, given a converging series of vectors in a finite-dimensional real vector space E, the set of sums of converging rearranged series is an affine subspace...

- then the series is absolutely convergent. If r > 1, then the series diverges. If r = 1, the ratio test is inconclusive, and the series may converge. This...

- mathematics, a series or integral is said to be conditionally convergent if it converges, but it does not converge absolutely. More precisely, a series ∑ n = 0...

- other function converging to a limit in a metric space. (See: Cauchy sequence; Limit of a sequence; Limit of a function.) Pointwise convergence Unconditional...

- mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions ( f n )...

- {\tfrac {1}{2}}\right).} The following two formulas involve quickly converging series, and are thus appropriate for numerical com****tion: G = 3 ∑ n = 0...

- number when the number of their terms increases. More precisely, a series converges, if there exists a number ℓ {\displaystyle \ell } such that for every...

- In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the...

- Convergence is a series of books edited by Ruth Nanda Anshen and published by the Columbia University Press dealing with ideas that changed, or that are...

- generally, given a converging series of vectors in a finite-dimensional real vector space E, the set of sums of converging rearranged series is an affine subspace...

- then the series is absolutely convergent. If r > 1, then the series diverges. If r = 1, the ratio test is inconclusive, and the series may converge. This...

- mathematics, a series or integral is said to be conditionally convergent if it converges, but it does not converge absolutely. More precisely, a series ∑ n = 0...

- other function converging to a limit in a metric space. (See: Cauchy sequence; Limit of a sequence; Limit of a function.) Pointwise convergence Unconditional...

- mathematical field of analysis, uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions ( f n )...

- {\tfrac {1}{2}}\right).} The following two formulas involve quickly converging series, and are thus appropriate for numerical com****tion: G = 3 ∑ n = 0...

- number when the number of their terms increases. More precisely, a series converges, if there exists a number ℓ {\displaystyle \ell } such that for every...

- In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the...

- Convergence is a series of books edited by Ruth Nanda Anshen and published by the Columbia University Press dealing with ideas that changed, or that are...

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