
'''simple docstring'''





from __future__ import annotations

def   A			(							A_				:       Tuple     ,				A_				:       Optional[Any]     ,				A_				:       str     ,				):


						if not all((nth_term, start_term_a, common_ratio_r)							):
												return []
						snake_case							:  list[float | int]			=     []
						snake_case							:  str			=     1
						snake_case							:  Union[str, Any]			=     common_ratio_r
						for _ in range(int(a_							)							):
												if not series:
																		series.append(a_							)
												else:
																		power += 1
																		series.append(float(start_term_a * multiple							)							)
																		snake_case							:  List[Any]			=     pow(float(a_							)     ,				a_							)
						return series


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						UpperCAmelCase            = float(input("Enter the last number (n term) of the Geometric Series"))
						UpperCAmelCase            = float(input("Enter the starting term (a) of the Geometric Series"))
						UpperCAmelCase            = 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))



"""simple docstring"""

def 						UpperCAmelCase   (						a_     ):





		'''simple docstring'''


		if not isinstance(a_,		a_     ):
				raise TypeError('recursive_lucas_number accepts only integer arguments.'     )
		if n_th_number == 0:
				return 2
		if n_th_number == 1:
				return 1

		return recursive_lucas_number(n_th_number - 1     ) + recursive_lucas_number(
		    n_th_number - 2     )
def 						UpperCAmelCase   (						a_     ):





		'''simple docstring'''


		if not isinstance(a_,		a_     ):
				raise TypeError('dynamic_lucas_number accepts only integer arguments.'     )
		lowerCamelCase      ,       lowerCamelCase	:     Optional[int]            =       2, 1
		for _ in range(a_     ):
				lowerCamelCase      ,       lowerCamelCase	:     Optional[int]            =       b, a + b
		return a


if __name__ == "__main__":
					from doctest import testmod

					testmod()
					_A				=					int(input('Enter the number of terms in lucas series:\n').strip())
					print('Using recursive function to calculate lucas series:')
					print(' '.join(str(recursive_lucas_number(i)) for i in range(n)))
					print('\nUsing dynamic function to calculate lucas series:')
					print(' '.join(str(dynamic_lucas_number(i)) for i in range(n)))






