Pi recursive

"""
The Leibniz formula for π is as follows:
π = 4 * (1 - 1/3 + 1/5 - 1/7 + 1/9 - ...)

More info at:
https://www.cuemath.com/calculus/leibniz-rule/

Watch out Python will throw an error at a key point.
"""

def calculate_pi(n, i=1, sum=0, sign=1):
    if n == 0:
        return 4 * sum
    else:
        term = sign * (1 / i)
        print(term)
        return calculate_pi(n - 1, i + 2, sum + term, -sign)

# Test the function
approx_pi = calculate_pi(800)  # Increase the number of iterations for a more accurate result
print(approx_pi)