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The exact value of the series is discovered by /-

The exact value of the series is discovered by /-

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Question:** The exact value of the series \(\sum_{n=1}^{\infty} \frac{1}{n^2}\) is _______ discovered by _______. **Explanation:** This question presents the mathematical series \( \sum_{n=1}^{\infty} \frac{1}{n^2} \), which is a well-known infinite series in the field of mathematics. The task is to identify its exact value and the person who discovered it. **Additional Information:** The series is recognized as the Basel problem, and its exact sum is an important result in mathematical analysis. The value of this series is \( \frac{\pi^2}{6} \). The discovery of this value was made by the famous mathematician Leonhard Euler. Therefore, the completed statement would be: The exact value of the series \(\sum_{n=1}^{\infty} \frac{1}{n^2}\) is \(\frac{\pi^2}{6}\) discovered by Leonhard Euler.
Transcribed Image Text:**Question:** The exact value of the series \(\sum_{n=1}^{\infty} \frac{1}{n^2}\) is _______ discovered by _______. **Explanation:** This question presents the mathematical series \( \sum_{n=1}^{\infty} \frac{1}{n^2} \), which is a well-known infinite series in the field of mathematics. The task is to identify its exact value and the person who discovered it. **Additional Information:** The series is recognized as the Basel problem, and its exact sum is an important result in mathematical analysis. The value of this series is \( \frac{\pi^2}{6} \). The discovery of this value was made by the famous mathematician Leonhard Euler. Therefore, the completed statement would be: The exact value of the series \(\sum_{n=1}^{\infty} \frac{1}{n^2}\) is \(\frac{\pi^2}{6}\) discovered by Leonhard Euler.
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