One infinite series used to calculate π (pi) is the Leibniz formula for π.
The Leibniz formula expresses π/4 as an alternating sum of the reciprocals of odd numbers. Specifically:
π/4 = 1/1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - ...
Therefore, to calculate π directly using this series:
π = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ...
While elegant, the Leibniz formula converges to π very slowly, meaning a significant number of terms are needed to achieve a reasonable level of accuracy. Many other, more efficient, infinite series exist for calculating pi to high degrees of precision.
