Key Ingredients:

k:
The term index in the summation.

(6k)!,(3k)!,k!(6k)!, (3k)!, k!(6k)!,(3k)!,k!:
Factorial terms, growing very quickly as k increases.

545140134 and 13591409:
Constants in the formula, arising from the mathematical derivation of the series.

640320^3k+3/2:
A large power of 640320 that helps ensure rapid convergence.

 

The multiplier 12 ensures that the sum gives the reciprocal of π.

Use in Computing π

The Chudnovsky algorithm is widely used in programs for computing millions or even trillions of digits of π/pi, leveraging its rapid convergence and ability to compute terms in parallel. The practical implementation often involves summing the series up to a finite number of terms, depending on the desired precision.

 

In practice, the algorithm is implemented with optimizations for factorial computations and large integer arithmetic to handle the immense size of the numbers involved in calculations.