#Pi using Leibniz's formula
def calculate_pi(iterations):
    pi_approximation = 0.0
    for i in range(iterations):
        term = 4.0 * (-1) ** i / (2 * i + 1)
        pi_approximation += term
    return pi_approximation

def compute_pi(iterations):
  pi_approx = 0.0
  for i in range(iterations):
      term=8.0/((4*i+1)*(4*i+3))
      pi_approx+=term
  return pi_approx

def estimate_pi(iterations):
    pi=0.0
    for i in range(iterations):
        term=3.0/((i+1)*(2*i+1)*(4*i+1))
        pi+=term
    return pi

# Number of iterations for approximation
iterations = 1000000
approx_pi = calculate_pi(iterations)
computed_pi=compute_pi(iterations)
pi=estimate_pi(iterations)
print(f"Approximation of pi after {iterations} iterations: {approx_pi}")
print(f"Approximation of pi after {iterations} iterations: {computed_pi}")
print(f"Approximation of pi after {iterations} iterations: {pi}")