from __future__ import annotations

def        SCREAMING_SNAKE_CASE_					(						snake_case__       ,  snake_case__       ,  snake_case__       ,  )					->     list[float | int]:
							if not all((nth_term, start_term_a, common_ratio_r)							):
														return []
							lowerCAmelCase     		=		[]
							lowerCAmelCase     		=		1
							lowerCAmelCase     		=		common_ratio_r
							for _ in range(int(snake_case__							)							):
														if not series:
																					series.append(snake_case__							)
														else:
																					power += 1
																					series.append(float(start_term_a * multiple							)							)
																					lowerCAmelCase     		=		pow(float(snake_case__							)       ,  snake_case__							)
							return series


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	lowercase__      :    Optional[Any]          =     float(input('''Enter the last number (n term) of the Geometric Series'''))
	lowercase__      :    List[Any]          =     float(input('''Enter the starting term (a) of the Geometric Series'''))
	lowercase__      :    Union[str, Any]          =     float(
	    input('''Enter the common ratio between two terms (r) of the Geometric Series''')
	)
	print('''Formula of Geometric Series => a + ar + ar^2 ... +ar^n''')
	print(geometric_series(nth_term, start_term_a, common_ratio_r))




import random




class        lowercase_  :



	"""simple docstring"""





	def __init__(							self		,      __SCREAMING_SNAKE_CASE		,      __SCREAMING_SNAKE_CASE    )						->None:
								lowerCAmelCase     		=		x
								lowerCAmelCase     		=		y


	def       SCREAMING_SNAKE_CASE_    (							self    )						->bool:
								return (self.x**2 + self.y**2) <= 1




	@classmethod
	def       SCREAMING_SNAKE_CASE_    (							cls    )						->Tuple:
								return cls(x=random.random()		,      y=random.random()    )

def        SCREAMING_SNAKE_CASE_					(						snake_case__							)					->     float:
							if number_of_simulations < 1:
														raise ValueError('''At least one simulation is necessary to estimate PI.'''							)

							lowerCAmelCase     		=		0
							for _ in range(snake_case__							):
														lowerCAmelCase     		=		Point.random_unit_square()

														if random_point.is_in_unit_circle():
																					number_in_unit_circle += 1

							return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
	# import doctest

	# doctest.testmod()
	from math import pi

	lowercase__      :    int          =     '''Please enter the desired number of Monte Carlo simulations: '''
	lowercase__      :    Dict          =     estimate_pi(int(input(prompt).strip()))
	print(f'An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}')



