On the Basel Problem and the Square of Gregory’s Series
Mathematics Magazine(2024)
摘要
the following question arises: Can this latter formula be derived by squaring both sides of the former? There have been several proofs of Euler's formula, or its equivalent formulation ζ(2)=π2/6, based on the idea of squaring 1−13+15−⋯=π4, including a proof presented in a letter from Euler to Goldbach dating from 1742. We consider the history of proofs of this form, and we offer another simple proof of ζ(2)=π2/6 that also relies on squaring Gregory's series.
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