
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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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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