08-09-2026, 08:27 AM
Basel problem
Summary
The Basel problem is a famous problem in mathematics that asks for the exact value of the infinite series $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^2}$. Although the series was easy to show to be convergent, finding its exact sum remained unsolved for nearly a century until Leonhard Euler proved in 1734 that $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$. Euler’s solution was significant because it connected an infinite sum involving integers with the geometric constant $\pi$, and his result became an important example of the power of infinite series and mathematical analysis. The Basel problem also led to further developments involving the Riemann zeta function, for which the result can be written as $\zeta(2)=\frac{\pi^2}{6}$.
ARTICLE
Summary
The Basel problem is a famous problem in mathematics that asks for the exact value of the infinite series $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^2}$. Although the series was easy to show to be convergent, finding its exact sum remained unsolved for nearly a century until Leonhard Euler proved in 1734 that $\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$. Euler’s solution was significant because it connected an infinite sum involving integers with the geometric constant $\pi$, and his result became an important example of the power of infinite series and mathematical analysis. The Basel problem also led to further developments involving the Riemann zeta function, for which the result can be written as $\zeta(2)=\frac{\pi^2}{6}$.
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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│ KONSTANTINOS MICHAILIDIS │
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