BBP formula in Python

See http://mathworld.wolfram.com/BBPFormula.html

Not the most efficient Python but it works.

def x(n):
    return (4.0/(8*n+1)-2.0/(8*n+4) - 1.0/(8*n+5) -1.0/(8*n+6))*((1.0/16)**n)

def pi(n):
    s = 0
    for i in range(n):
        s+=x(i)
    return s

>>> pi(1)
3.1333333333333333
>>> pi(2)
3.1414224664224664
>>> pi(4)
3.1415924575674357
>>> pi(10)
3.1415926535897913
>>> pi(20)
3.141592653589793
>>> pi(40)
3.141592653589793

 

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