TRES SERIES FAMOSAS EN LA HISTORIA DE LA MATEMÁTICA

José Antonio Camarena Berrío; Ángela Yaneth Franco

doi:10.48204/j.colegiada.v5n2.a5026

Submitted April 24, 2024

Published 2024-04-24

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Vol. 5 No. 2 (2024): Revista Colegiada de Ciencia

THREE FAMOUS SERIES IN THE HISTORY OF THE MATHEMATICS

José Antonio Camarena Berrío ⁺⁻
Ángela Yaneth Franco ⁺⁻

DOI https://doi.org/10.48204/j.colegiada.v5n2.a5026

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DOI: 10.48204/j.colegiada.v5n2.a5026

Published: 2024-04-24

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Camarena Berrío , J. A., & Franco , Ángela Y. (2024). THREE FAMOUS SERIES IN THE HISTORY OF THE MATHEMATICS. Revista Colegiada De Ciencia, 5(2), 70–87. https://doi.org/10.48204/j.colegiada.v5n2.a5026

Abstract

The harmonic, alternated harmonic and –series with (Basel problem) series,

are some of the most famous infinite series in mathematics and, they are used as examples and counterexamples to illustrate the theory of convergence of series. In this article some of the contributions of the mathematicians who dedicated themselves to the study of the convergence of these three series are presented. The contributions of Nicole Oresme, Pietro Mengoli, Nikolaus Mercator and Leonhard Euler are highlighted.

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References

Apostol, T. M. (1983). A Proof that Euler Missed, Evaluating ? (2) the Easy Way. The Mathematical Intelligencer. 5(3). 59-60.
Bell, J. y. Blasjo, V. (2018). Pietro Mengoli's 1650 Proof that the Harmonic Series Diverges. Mathematics Magazine. 91(5). 341-347.
Dunham. W. (1999). Euler: The Master of Us All. The American Mathematical Society.
Dunham. W. (2007). The Genius of Euler: Reflections on his life and work. The Mathematical Association of American.
Apostol, T. M. (1983). A Proof that Euler Missed, Evaluating ? (2) the Easy Way. The Mathematical Intelligencer. 5(3). 59-60.
Bell, J. y. Blasjo, V. (2018). Pietro Mengoli's 1650 Proof that the Harmonic Series Diverges. Mathematics Magazine. 91(5). 341-347.
Dunham. W. (1999). Euler: The Master of Us All. The American Mathematical Society.
Dunham. W. (2007). The Genius of Euler: Reflections on his life and work. The Mathematical Association of American.
Dunham, W. (2018). The Calculus Gallery: Masterpieces from Newton to Lebesgue. Princeton University Press.
Edward, C. H. (1994). The Historical Dvelopment of the calculus. Springer.
Hassler, U. y Hossein Kouchack, M. (2022). Basel Problem: Historical perspective and futher proofs from stochastic processes. Euleriana. 2(2). 120 -130.
Kalman, D. (1993). Six Ways to Sum a Series. The College Mathematics Jounal. 24(5). 402-421.
Komornik, V. (2022). A "Luminous" Solution to the Basel Problem. Mathematics Magazine: 95(4). 333-337.
Komornik, V. y Schafke, R. (2021). Leibniz, Newton, and Cauchy; A Complex Relationship. The American Mathematical Monthly. 128(4). 367-369.
Russell, D.C. (1991). Another Eulerian-Type Proof. Mathematics Magazine. 64(5). 349-349.

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[1] Apostol, T. M. (1983). A Proof that Euler Missed, Evaluating ? (2) the Easy Way. The Mathematical Intelligencer. 5(3). 59-60.

[2] Bell, J. y. Blasjo, V. (2018). Pietro Mengoli's 1650 Proof that the Harmonic Series Diverges. Mathematics Magazine. 91(5). 341-347.

[3] Dunham. W. (1999). Euler: The Master of Us All. The American Mathematical Society.

[4] Dunham. W. (2007). The Genius of Euler: Reflections on his life and work. The Mathematical Association of American.

[5] Apostol, T. M. (1983). A Proof that Euler Missed, Evaluating ? (2) the Easy Way. The Mathematical Intelligencer. 5(3). 59-60.

[6] Bell, J. y. Blasjo, V. (2018). Pietro Mengoli's 1650 Proof that the Harmonic Series Diverges. Mathematics Magazine. 91(5). 341-347.

[7] Dunham. W. (1999). Euler: The Master of Us All. The American Mathematical Society.

[8] Dunham. W. (2007). The Genius of Euler: Reflections on his life and work. The Mathematical Association of American.

[9] Dunham, W. (2018). The Calculus Gallery: Masterpieces from Newton to Lebesgue. Princeton University Press.

[10] Edward, C. H. (1994). The Historical Dvelopment of the calculus. Springer.

[11] Hassler, U. y Hossein Kouchack, M. (2022). Basel Problem: Historical perspective and futher proofs from stochastic processes. Euleriana. 2(2). 120 -130.

[12] Kalman, D. (1993). Six Ways to Sum a Series. The College Mathematics Jounal. 24(5). 402-421.

[13] Komornik, V. (2022). A "Luminous" Solution to the Basel Problem. Mathematics Magazine: 95(4). 333-337.

[14] Komornik, V. y Schafke, R. (2021). Leibniz, Newton, and Cauchy; A Complex Relationship. The American Mathematical Monthly. 128(4). 367-369.

[15] Russell, D.C. (1991). Another Eulerian-Type Proof. Mathematics Magazine. 64(5). 349-349.

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