Log in

Relevant bibliographies by topics / Sum of the series / Journal articles

To see the other types of publications on this topic, follow the link: Sum of the series.

Journal articles on the topic 'Sum of the series'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Sum of the series.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Kraines, David P., Vivian Y. Kraines, and David A. Smith. "Sum the Alternating Harmonic Series." College Mathematics Journal 20, no. 5 (1989): 433. http://dx.doi.org/10.2307/2686934.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

de Bruijn, N. G., and Rolf Richberg. "Sum of a Series: 11131." American Mathematical Monthly 113, no. 7 (2006): 661. http://dx.doi.org/10.2307/27642024.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Sahadat Sarkar, Najmuj. "The Sum of Fibionacci Series." International Journal of Mathematics and Statistics Invention 13, no. 2 (2025): 01–03. https://doi.org/10.35629/4767-13020103.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Laszlo, Akos. "The Sum of Some Convergent Series." American Mathematical Monthly 108, no. 9 (2001): 851. http://dx.doi.org/10.2307/2695557.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Ramirez, Oscar Ciaurri, and Daniele Donini. "Sum of an Infinite Series: 10867." American Mathematical Monthly 109, no. 6 (2002): 575. http://dx.doi.org/10.2307/2695460.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Kalman, Dan. "Six Ways to Sum a Series." College Mathematics Journal 24, no. 5 (1993): 402. http://dx.doi.org/10.2307/2687013.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Fomin, V. I. "About One Designation of Series Sum." Voprosy sovremennoj nauki i praktiki. Universitet imeni V.I. Vernadskogo, no. 2(64) (2017): 157–59. http://dx.doi.org/10.17277/voprosy.2017.02.pp.157-159.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Harper, James D. "Estimating the Sum of Alternating Series." College Mathematics Journal 19, no. 2 (1988): 149. http://dx.doi.org/10.2307/2686176.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

Kholshchevnikova, N. N. "Sum of Everywhere Convergent Trigonometric Series." Mathematical Notes 75, no. 3/4 (2004): 439–43. http://dx.doi.org/10.1023/b:matn.0000023326.92961.ce.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Harper, James D. "Estimating the Sum of Alternating Series." College Mathematics Journal 19, no. 2 (1988): 149–53. http://dx.doi.org/10.1080/07468342.1988.11973103.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Gorfin, Alan. "Evaluating the Sum of the Series." College Mathematics Journal 20, no. 4 (1989): 329–31. http://dx.doi.org/10.1080/07468342.1989.11973254.

Full text

APA, Harvard, Vancouver, ISO, and other styles

12

Kalman, Dan. "Six Ways to Sum a Series." College Mathematics Journal 24, no. 5 (1993): 402–21. http://dx.doi.org/10.1080/07468342.1993.11973562.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Chelidze, G., G. Giorgobiani, and V. Tarieladze. "Sum Range of a Quaternion Series." Journal of Mathematical Sciences 216, no. 4 (2016): 519–21. http://dx.doi.org/10.1007/s10958-016-2908-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

László, Ákos. "The Sum of Some Convergent Series." American Mathematical Monthly 108, no. 9 (2001): 851–55. http://dx.doi.org/10.1080/00029890.2001.11919819.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Kadets, V. M. "Sum regions of weakly convergent series." Functional Analysis and Its Applications 23, no. 2 (1989): 133–35. http://dx.doi.org/10.1007/bf01078784.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

Plaza, Ágnel. "Proof without words: partial sum and sum of a geometric series." Teaching Mathematics and Computer Science 2, no. 2 (2015): 423. http://dx.doi.org/10.5485/tmcs.2004.0075.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Tetunashvili, Sh. "Functional series representable as a sum of two universal series." Doklady Mathematics 96, no. 3 (2017): 578–79. http://dx.doi.org/10.1134/s106456241706014x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Ash, Kute. "Ramanujan Sum of All Natural Numbers without Grandi Series." International Journal of Science and Research (IJSR) 13, no. 4 (2024): 1326–27. http://dx.doi.org/10.21275/sr24321135426.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Virtanen, Jouko J. "85.05 Using Intuition to Sum a Series." Mathematical Gazette 85, no. 502 (2001): 86. http://dx.doi.org/10.2307/3620477.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Abramov, Vyachslav. "Evaluating the sum of convergent positive series." Publications de l'Institut Math?matique (Belgrade) 111, no. 125 (2022): 41–53. http://dx.doi.org/10.2298/pim2225041a.

Full text

Abstract:

We provide numerical procedures for possibly best evaluating the sum of positive series under quite general setting. Our procedures are based on the application of a generalized version of Kummer's test.

APA, Harvard, Vancouver, ISO, and other styles

21

Paudyal, Daya Ram, and Lakshmi Narayan Mishra. "ON APPROXIMATION OF SUM OF CONVERGENT SERIES." Journal of Engineering and Exact Sciences 6, no. 3 (2020): 0421–28. http://dx.doi.org/10.18540/jcecvl6iss3pp0421-0428.

Full text

Abstract:

The paper has given a clear opinion on the progress of environmental protection and sustainability in the Nigerian context. The environmental regulations scenario in the country is marred by malpractices and corruption more stringent policy enforcement will help in the achievement of environmental protection. This paper deals with a specialized method of approximating the sum of an infinite series containing positive terms which are monotonically decreasing. The analysis has been done by taking some references done by the great mathematician Leonhard Euler with some special examples. Consequen

APA, Harvard, Vancouver, ISO, and other styles

22

白, 颖. "Convergence and Sum Function of Power Series." Advances in Applied Mathematics 09, no. 08 (2020): 1221–29. http://dx.doi.org/10.12677/aam.2020.98143.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Carlson, G. T., and B. L. Illman. "Series capacitors and the inverse sum rule." American Journal of Physics 70, no. 11 (2002): 1122–28. http://dx.doi.org/10.1119/1.1506170.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Chan, Song Heng, and Byungchan Kim. "On some double-sum false theta series." Journal of Number Theory 190 (September 2018): 40–55. http://dx.doi.org/10.1016/j.jnt.2018.02.012.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Igarashi, Masahiro. "Cyclic sum of certain parametrized multiple series." Journal of Number Theory 131, no. 3 (2011): 508–18. http://dx.doi.org/10.1016/j.jnt.2010.09.011.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Wituła, Roman, and Damian Słota. "On the sum of some alternating series." Computers & Mathematics with Applications 62, no. 6 (2011): 2658–64. http://dx.doi.org/10.1016/j.camwa.2011.08.008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Sheremeta, Myroslav Mykolayovych, Yulia Vasylivna Stets, and Oksana Markiyanivna Sumyk. "Estimates of a sum of Dirichlet series." Journal of Mathematical Sciences 194, no. 5 (2013): 557–72. http://dx.doi.org/10.1007/s10958-013-1546-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Scott, J. A. "98.12 A convergent series with zero sum." Mathematical Gazette 98, no. 542 (2014): 325–27. http://dx.doi.org/10.1017/s0025557200001388.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Reynolds, Robert, and Allan Stauffer. "Extended de Montmort-Prudnikov Sum." Mathematics 11, no. 2 (2023): 333. http://dx.doi.org/10.3390/math11020333.

Full text

Abstract:

Using a contour integral method, the de Montmort-Prudnikov sum is extended to derive a new series representation involving the incomplete gamma function. The series is uniformly convergent and completely analytical, which can be evaluated for general complex ranges of the parameters involved. Applications and evaluations of this formula are discussed.

APA, Harvard, Vancouver, ISO, and other styles

30

Stojiljkovic, Vuk. "Series involving Dirichlet Eta function." Gulf Journal of Mathematics 15, no. 1 (2023): 67–83. http://dx.doi.org/10.56947/gjom.v15i1.1135.

Full text

Abstract:

In this article, we obtain an integral representation for a remainder sum of the Dirichlet Eta function. We then obtain numerous generating functions and series concerning the usage of the obtained integral representation. Alternating Fibonacci sum of the partial sum of the Dirichlet Eta function has been obtained, as well as the squared version Fibonacci series concerning the sum. A generalized representation of the product of polynomials concerning the partial sum of the Dirichlet Eta function has been obtained. Numerous examples have been provided to showcase the derived results.

APA, Harvard, Vancouver, ISO, and other styles

31

Patel, Gaurav Singh, and Saurabh Kumar Gautam. "Ramanujan: The New Sum of All Natural Numbers." International Journal for Research in Applied Science and Engineering Technology 10, no. 2 (2022): 1272–74. http://dx.doi.org/10.22214/ijraset.2022.40511.

Full text

Abstract:

Abstract: As we know that Sir Ramanujan gave the solution of sum of all natural numbers up to infinity and said that the sum of all natural numbers till infinity is -1/12. I studied on this topic and found that if we try to solve the infinite series in a slightly different way, then we get the answer of its sum different from -1/12, so this is what I have written in this paper that such Ramanujan Sir, what was the mistake in solving the infinite series, which by solving it in a slightly different way from the same concept, we get different answers. Keywords: Ramanujan the new sum of all natura

APA, Harvard, Vancouver, ISO, and other styles

32

NASH-WILLIAMS, C. St J. A., and D. J. WHITE. "Rearrangement of vector series. II." Mathematical Proceedings of the Cambridge Philosophical Society 130, no. 1 (2001): 111–34. http://dx.doi.org/10.1017/s0305004100004825.

Full text

Abstract:

Let [sum ]∞an denote the set of cluster points of the sequence of partial sums of a series [sum ]an with terms in ℝd. For any permutation f of the set ℕ of positive integers, [Cscr ]f (ℝd) denotes the set of all sets [sum ]∞af(n) arising from series [sum ]an with terms in ℝd and sum 0. For each f, we use the Max-Flow Min-Cut Theorem to determine all convex sets in [Cscr ]f(ℝd) which are symmetric about a point. These sets depend only on a parameter w(f) ∈ ℕ ∪ {0, ∞}, called the width of f. We show that w(f), when it is a positive integer, falls far short of completely determining [Cscr ]f(ℝd)

APA, Harvard, Vancouver, ISO, and other styles

33

S, Sriram, and David Christopher A. "Raising Series to A Power." Indian Journal of Science and Technology 17, SP1 (2024): 124–35. https://doi.org/10.17485/IJST/v17sp1.249.

Full text

Abstract:

Abstract <strong>Objective.</strong> Let be a formal power series and let . In this note, we consider the function . We find that if has a series expansion at , then its coefficients are polynomials in . The coefficients of these polynomials were found to be a weighted composition sum. <strong>Methods.</strong> The method to arrive at this representation involves logarithmic derivative and exponential representation. <strong>Findings.</strong> As a consequence of this, new identities involving partition functions and binomial coefficients were obtained. Further, a part

APA, Harvard, Vancouver, ISO, and other styles

34

Rungratgasame, Thitarie, and Punna Charrasangsakul. "Partial-Sum Matrix and its Rank." WSEAS TRANSACTIONS ON MATHEMATICS 22 (October 20, 2023): 768–72. http://dx.doi.org/10.37394/23206.2023.22.84.

Full text

Abstract:

A partial-sum matrix is a matrix whose entries are partial sums of a seires associate with a sequence. The rank of a partial-sum matrix associate with any recurrence sequence can be related to the rank of an associate recurrence matrix, a matrix whose entries are from the same recurrence sequence. In particular, we find ranks of partial-sum matrices associated with arithmetic series and geometric series.

APA, Harvard, Vancouver, ISO, and other styles

35

Sriram, S., and A. David Christopher. "Raising Series to A Power." Indian Journal Of Science And Technology 17, SPI1 (2024): 124–35. http://dx.doi.org/10.17485/ijst/v17sp1.249.

Full text

Abstract:

Objective. Let be a formal power series and let . In this note, we consider the function . We find that if has a series expansion at , then its coefficients are polynomials in . The coefficients of these polynomials were found to be a weighted composition sum. Methods. The method to arrive at this representation involves logarithmic derivative and exponential representation. Findings. As a consequence of this, new identities involving partition functions and binomial coefficients were obtained. Further, a particular class of Dirichlet series is found to have the form of an exponential function

APA, Harvard, Vancouver, ISO, and other styles

36

Rudin, Walter. "Power series with zero-sum on countable sets." Complex Variables, Theory and Application: An International Journal 18, no. 3-4 (1992): 283–84. http://dx.doi.org/10.1080/17476939208814553.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Lin, De-Hone. "Path integral solution by sum over perturbation series." Journal of Mathematical Physics 41, no. 5 (2000): 2723–31. http://dx.doi.org/10.1063/1.533266.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Unal, Hasan. "Proof Without Words: Sum of an Infinite Series." College Mathematics Journal 40, no. 1 (2009): 39. http://dx.doi.org/10.1080/07468342.2009.11922334.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

An, Yajun, and Tom Edgar. "“Sum” Visual Rearrangements of the Alternating Harmonic Series." College Mathematics Journal 50, no. 4 (2019): 280–85. http://dx.doi.org/10.1080/07468342.2019.1655375.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Li, Zhonghua, and Ende Pan. "Sum of interpolated finite multiple harmonic q-series." Journal of Number Theory 201 (August 2019): 148–75. http://dx.doi.org/10.1016/j.jnt.2019.02.024.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Greene, J., and D. Stanton. "A character sum evaluation and Gaussian hypergeometric series." Journal of Number Theory 23, no. 1 (1986): 136–48. http://dx.doi.org/10.1016/0022-314x(86)90009-0.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Krivosheev, Aleksandr Sergeevich, and Olesya Aleksandrovna Krivosheeva. "A closedness of set of Dirichlet series sum." Ufimskii Matematicheskii Zhurnal 5, no. 3 (2013): 94–117. http://dx.doi.org/10.13108/2013-5-3-94.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Unal, Hasan. "Proof Without Words: Sum of an Infinite Series." College Mathematics Journal 40, no. 1 (2009): 39. http://dx.doi.org/10.4169/193113409x469695.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Jaraldpushparaj, S., and G. Britto Antony Xavier. "Extended Mittag-Leffler function, series and its sum." Journal of Physics: Conference Series 1597 (July 2020): 012005. http://dx.doi.org/10.1088/1742-6596/1597/1/012005.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Shen, Lu-Ming, and Jun Wu. "On the error-sum function of Lüroth series." Journal of Mathematical Analysis and Applications 329, no. 2 (2007): 1440–45. http://dx.doi.org/10.1016/j.jmaa.2006.07.049.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Makarov, V. Yu. "Characteristics of the sum of a multidimensional series." Ukrainian Mathematical Journal 46, no. 7 (1994): 971–78. http://dx.doi.org/10.1007/bf01056674.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Sangarsu, Raghaven Rao. "Ramanujan Sums of All Natural Numbers with Grandi Series." Journal of Research in Vocational Education 6, no. 9 (2024): 3–4. http://dx.doi.org/10.53469/jrve.2024.6(09).02.

Full text

Abstract:

We are all know that the Ramanujan’s theory of calculating the sum of all the natural number. When we came to known that sum of all-natural number is ,that time everyone thinks about two things, one is how it possible that sum of positive number is negative & other is how it is very close to zero. Another research paper gives value of all natural number is then I started the study of this sum, then I find it is as zero. Quit interestingly but this value has more important than Ramanujan’s sum because I did not consider the Grandi series for calculating this sum. And then it is very easy to

APA, Harvard, Vancouver, ISO, and other styles

48

Chen, Chang-Pao. "L1-convergence of Fourier series." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 3 (1986): 376–90. http://dx.doi.org/10.1017/s144678870003384x.

Full text

Abstract:

AbstractFor an integrable function f on T, we introduce a modified partial sum and establish its L1-convergence property. The relation between the sum and L1-convergence classes is also established. As a corollary, a new L1-convergence class is obtained. It is shown that this class covers all known L1-convergence classes.

APA, Harvard, Vancouver, ISO, and other styles

49

Nurcombe, J. R. "Alteration in the sum of alternating series by simple rearrangement." Mathematical Gazette 97, no. 539 (2013): 193–97. http://dx.doi.org/10.1017/s0025557200005763.

Full text

Abstract:

It is well known that the sum of an absolutely convergent series is invariant under rearrangement of its terms. On the other hand, a conditionally convergent series, that is one which converges but the sum of whose absolute values is unbounded, can be rearranged to have any sum whatsoever, or diverge in any desired manner (see for example [1, §44]). A simple examplS of a conditionally convergent series is the alternating harmonic series (AHS), . In [2], the following theorem on rearrangement of the AHS was proved:Theorem A: The AHS remains convergent under a simple rearrangement (i.e. the sub-

APA, Harvard, Vancouver, ISO, and other styles

50

NASH-WILLIAMS, C. St J. A., and D. J. WHITE. "Rearrangement of vector series. I." Mathematical Proceedings of the Cambridge Philosophical Society 130, no. 1 (2001): 89–109. http://dx.doi.org/10.1017/s0305004100004813.

Full text

Abstract:

Let ℝd* = ℝd ∪ {[midast ]} be the one-point compactification of Euclidean space ℝd and d [ges ] 2. Given a permutation f of the set ℕ of positive integers, let [Cscr ]f(ℝd*) denote the set of all sets C ⊆ ℝd* for which there is a series [sum ]an in ℝd with zero sum such that C is the cluster set in ℝd* of the sequence of partial sums of [sum ]af(n). Every C ∈ [Cscr ]f(ℝd*) is non-empty, connected and closed in ℝd*. We give a combinatorial characterization of the permutations f for which all non-empty closed connected subsets of ℝd* belong to [Cscr ]f(ℝd*). For every permutation f of ℕ, we dete

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!