





from __future__ import annotations





def     lowerCamelCase__  (  UpperCamelCase__      :							float | int							,     UpperCamelCase__      :							float | int							,     UpperCamelCase__      :							float | int							,     )      ->			list[float | int]:



					'''simple docstring'''




					if not all((nth_term, start_term_a, common_ratio_r)    ):
										return []
					_snake_case						=					[]
					_snake_case						=					1
					_snake_case						=					common_ratio_r
					for _ in range(int(UpperCamelCase__    )    ):
										if not series:
															series.append(UpperCamelCase__    )
										else:
															power += 1
															series.append(float(start_term_a * multiple    )    )
															_snake_case						=					pow(float(UpperCamelCase__    )							,     UpperCamelCase__    )
					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))










import math
from timeit import timeit





def     lowerCamelCase__  (  UpperCamelCase__      :							int    )      ->			int:



					'''simple docstring'''




					_snake_case						=					0
					_snake_case						=					abs(UpperCamelCase__    )
					while True:
										_snake_case						=					n // 10
										digits += 1
										if n == 0:
															break
					return digits





def     lowerCamelCase__  (  UpperCamelCase__      :							int    )      ->			int:



					'''simple docstring'''




					return 1 if n == 0 else math.floor(math.log(abs(UpperCamelCase__    )							,     10    ) + 1    )





def     lowerCamelCase__  (  UpperCamelCase__      :							int    )      ->			int:



					'''simple docstring'''




					return len(str(abs(UpperCamelCase__    )    )    )





def     lowerCamelCase__  (  )      ->			None:



					'''simple docstring'''




					from collections.abc import Callable

					def benchmark_a_function(UpperCamelCase__      :							Callable							,     UpperCamelCase__      :							int    ) -> None:
										_snake_case						=					F'''{func.__name__}({value})'''
										_snake_case						=					timeit(F'''__main__.{call}'''							,     setup='import __main__'    )
										print(F'''{call}: {func(UpperCamelCase__    )} -- {timing} seconds'''    )

					for value in (262_144, 1_125_899_906_842_624, 1_267_650_600_228_229_401_496_703_205_376):
										for func in (num_digits, num_digits_fast, num_digits_faster):
															benchmark_a_function(UpperCamelCase__							,     UpperCamelCase__    )
										print()


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					benchmark()



