summable series
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Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.[1] In mathematics, given an infinite sequence of numbers { an } … Wikipedia
summable — summability, n. /sum euh beuhl/, adj. Math. 1. capable of being added. 2. (of an infinite series, esp. a divergent one) capable of having a sum assigned to it by a method other than the usual one of taking the limit of successive partial sums. 3 … Universalium
History of Grandi's series — Geometry and infinite zerosGrandiGuido Grandi (1671 – 1742) reportedly provided a simplistic account of the series in 1703. He noticed that inserting parentheses into nowrap|1=1 − 1 + 1 − 1 + · · · produced varying results: either:(1 1) + (1 1) + … Wikipedia
Summation of Grandi's series — General considerationstability and linearityThe formal manipulations that lead to 1 − 1 + 1 − 1 + · · · being assigned a value of 1⁄2 include: *Adding or subtracting two series term by term, *Multiplying through by a scalar term by term, *… … Wikipedia
Convergence of Fourier series — In mathematics, the question of whether the Fourier series of a periodic function converges to the given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics. Convergence is not necessarily a given… … Wikipedia
Fourier series — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms … Wikipedia
Divergent geometric series — In mathematics, an infinite geometric series of the form is divergent if and only if | r | ≥ 1. Methods for summation of divergent series are sometimes useful, and usually evaluate divergent geometric series to a sum that… … Wikipedia
Lambert series — In mathematics, a Lambert series, named for Johann Heinrich Lambert, is a series taking the form:S(q)=sum {n=1}^infty a n frac {q^n}{1 q^n}It can be resummed formally by expanding the denominator::S(q)=sum {n=1}^infty a n sum {k=1}^infty q^{nk} … Wikipedia
absolutely summable — adjective An infinite series is absolutely summable if the sum of the absolute values of its summands converges … Wiktionary
1 − 2 + 3 − 4 + · · · — In mathematics, 1 − 2 + 3 − 4 + … is the infinite series whose terms are the successive positive integers, given alternating signs. Using sigma summation notation the sum of the first m terms of the series can be expressed as:sum {n=1}^m n( 1)^{n … Wikipedia
1 − 2 + 4 − 8 + · · · — In mathematics, 1 − 2 + 4 − 8 + hellip; is the infinite series whose terms are the successive powers of two with alternating signs. As a geometric series, it is characterized by its first term, 1, and its common ratio, −2. :sum {i=0}^{n} ( 2)^iAs … Wikipedia
