TRES SERIES FAMOSAS EN LA HISTORIA DE LA MATEMÁTICA

José Antonio Camarena Berrío; Ángela Yaneth Franco

doi:10.48204/j.colegiada.v5n2.a5026

Enviado abril 24, 2024

Publicado 2024-04-24

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v. 5 n. 2 (2024): Revista Colegiada de Ciencia

TRES SERIES FAMOSAS EN LA HISTORIA DE LA MATEMÁTICA

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

Publicado: 2024-04-24

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Camarena Berrío , J. A., & Franco , Ángela Y. (2024). TRES SERIES FAMOSAS EN LA HISTORIA DE LA MATEMÁTICA. Revista Colegiada De Ciencia, 5(2), 70–87. https://doi.org/10.48204/j.colegiada.v5n2.a5026

Resumo

Las series armónica, armónica alternada y –serie con . (problema de Basilea),

son unas de las series infinitas más célebres de la matemática. Ellas se usan como ejemplos y contraejemplos para ilustrar la teoría de la convergencia de series. En este artículo, se presentan algunas de las contribuciones de los matemáticos que se dedicaron al estudio de la convergencia de estas tres series; resaltando los aportes de Nicole Oresme, Pietro Mengoli, Nikolaus Mercator y Leonhard Euler.

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Referências

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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