


'''simple docstring'''

from __future__ import annotations






def __UpperCamelCase (      __lowerCamelCase		:			str					)   ->  bool:







     '''simple docstring'''






     _a            =		42
     _a            =		list(__lowerCamelCase					)
     _a      ,      _a            =		_vector[:-1], int(_vector[-1]					)
     _a            =		[int(__lowerCamelCase					) for digit in __vector]

     vector.reverse()
     for i, digit in enumerate(__lowerCamelCase					):
          if i & 1 == 0:
               _a            =		digit * 2
               if doubled > 9:
                    doubled -= 9
               check_digit += doubled
          else:
               check_digit += digit

     return check_digit % 10 == 0


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   assert is_luhn("79927398713")
   assert not is_luhn("79927398714")





'''simple docstring'''

from __future__ import annotations






def __UpperCamelCase (      __lowerCamelCase		:			float | int   ,	__lowerCamelCase		:			float | int   ,	__lowerCamelCase		:			float | int   ,	)   ->  list[float | int]:







     '''simple docstring'''






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


if __name__ == "__main__":
   import doctest

   doctest.testmod()

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

