It works as follows:
Then ak converges quartically against 1/π; that is, each iteration approximately quadruples the number of correct digits.
See also
... of the town is 40.00% White, 48.41% African American, 0.30% Native American, 3.41% Asian, 0.00% Pacific Islander, 4.15% from other races, and 3.73% from two or mo ...