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September 12, 2025Open Access

A new elementary proof of the formula ∑ₙ₌₁∞1/n²=π²/6

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Key Points

The method reveals a new approach to deriving the value of the infinite series sum.
It confirms that the sum of the reciprocals of the squares converges to π²/6.
This proof does not rely on complex analysis techniques, simplifying understanding.
Elementary proofs strengthen foundational knowledge in mathematical series and convergence.

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Implication

This article presents an elementary proof of the Basel problem formula, highlighting convergence properties.

Abstract

In this article, we provide a new elementary proof of the Basel problem.

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Cite This Study

Jia Li (2025) studied this question.

synapsesocial.com/papers/68e861b07ef2f04ca37e4b38 https://doi.org/10.48550/arxiv.2510.03233

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