Leibniz formula for π

See List of things named after Gottfried Leibniz for other formulas known under the same name.

In mathematics, the Leibniz formula for $π$ , named after Gottfried Leibniz, states that

1 \,-\, \frac{1}{3} \,+\, \frac{1}{5} \,-\, \frac{1}{7} \,+\, \frac{1}{9} \,-\, \cdots \;=\; \frac{\pi}{4}.\!

Using summation notation:

\sum_{n=0}^\infty \, \frac{(-1)^n}{2n+1} \;=\; \frac{\pi}{4}.\!

单词	Leibniz Series
释义	Leibniz Series 英语百科 Leibniz formula for π See List of things named after Gottfried Leibniz for other formulas known under the same name. In mathematics, the Leibniz formula for $π$ , named after Gottfried Leibniz, states that $1 \,-\, \frac{1}{3} \,+\, \frac{1}{5} \,-\, \frac{1}{7} \,+\, \frac{1}{9} \,-\, \cdots \;=\; \frac{\pi}{4}.\!$ Using summation notation: $\sum_{n=0}^\infty \, \frac{(-1)^n}{2n+1} \;=\; \frac{\pi}{4}.\!$
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Leibniz Series