Concise Proof of the Gregory-Leibniz Series

Posted: 2025-05-03 06:16:31 UTC

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This article contains some claims that remain unverified. While much of the content may be accurate, exercise care when relying on this information.

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2025-05-03 06:16:53 UTC

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This is a one-page proof of the Gregory-Leibniz Series, which provides a formula for calculating pi.

Proof of Gregory-Leibniz Series

Taylor series expansion

Variable substitution

Integration to find Taylor expansion of tan^-1(x)

Substitution of x=1 to derive the series for pi