

from __future__ import annotations

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


if __name__ == "__main__":
     import doctest

     doctest.testmod()

     _lowerCamelCase							:  str     =				float(input("Enter the last number (n term) of the Geometric Series"))
     _lowerCamelCase							:  Tuple     =				float(input("Enter the starting term (a) of the Geometric Series"))
     _lowerCamelCase							:  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))








def      a__	(						UpperCAmelCase				:     list     )    ->		list:
  UpperCAmelCase			:				Tuple										=					len(UpperCAmelCase     )

  # Set the gap value to be decreased by a factor of 1.3
  # after each iteration
  UpperCAmelCase			:				Optional[Any]										=					1.3

  # Continue sorting until the gap is 1
  while gap > 1:
    # Decrease the gap value
    UpperCAmelCase			:				int										=					int(gap / shrink     )

    # Sort the elements using insertion sort
    for i in range(UpperCAmelCase							,					len(UpperCAmelCase     )     ):
      UpperCAmelCase			:				Union[str, Any]										=					collection[i]
      UpperCAmelCase			:				List[Any]										=					i
      while j >= gap and collection[j - gap] > temp:
        UpperCAmelCase			:				int										=					collection[j - gap]
        j -= gap
      UpperCAmelCase			:				List[Any]										=					temp

  return collection


if __name__ == "__main__":
     import doctest

     doctest.testmod()





