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The Paradox of 1 — 1 + 1 — 1 + 1 — 1 + ...
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- Author(s): MURTAGH, JACK (AUTHOR)
- Source:
Scientific American. Oct2024, Vol. 331 Issue 3, p58-59. 2p.
- Additional Information
- Subject Terms:
- Abstract:
The article explores the paradox of the infinite series 1 - 1 + 1 - 1 + 1 - 1 + ... and the different conclusions reached by mathematicians throughout history. The series can be interpreted to sum to 0, 1, or 1/2, depending on how the parentheses are arranged. Mathematicians like Luigi Guido Grandi, Gottfried Wilhelm Leibniz, and Leonhard Euler offered different arguments for each interpretation. Ultimately, modern mathematicians conclude that the series does not sum to anything, but alternative methods of summation can assign a value of 1/2 to it. The article also discusses the concept of convergence in infinite series and the different definitions and methods of summation used in mathematics. [Extracted from the article]
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