





from __future__ import annotations
def     A__					(						SCREAMING_SNAKE_CASE_      :			List[str]							,  SCREAMING_SNAKE_CASE_      :			List[Any]							,  SCREAMING_SNAKE_CASE_      :			Any							,  )     ->     list[float | int]:






   """simple docstring"""







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






def     A__					(						SCREAMING_SNAKE_CASE_      :			list	)     ->     bool:






   """simple docstring"""







   if not isinstance(SCREAMING_SNAKE_CASE_							,  SCREAMING_SNAKE_CASE_	):
      raise ValueError('''Input series is not valid, valid series - [1, 2/3, 2]'''	)
   if len(SCREAMING_SNAKE_CASE_	) == 0:
      raise ValueError('''Input list must be a non empty list'''	)
   if len(SCREAMING_SNAKE_CASE_	) == 1 and series[0] != 0:
      return True
   _UpperCAmelCase											=      []
   _UpperCAmelCase											=      len(SCREAMING_SNAKE_CASE_	)
   for i in range(0							,  SCREAMING_SNAKE_CASE_	):
      if series[i] == 0:
         raise ValueError('''Input series cannot have 0 as an element'''	)
      rec_series.append(1 / series[i]	)
   _UpperCAmelCase											=      rec_series[1] - rec_series[0]
   for index in range(2							,  SCREAMING_SNAKE_CASE_	):
      if rec_series[index] - rec_series[index - 1] != common_diff:
         return False
   return True
def     A__					(						SCREAMING_SNAKE_CASE_      :			list	)     ->     float:






   """simple docstring"""







   if not isinstance(SCREAMING_SNAKE_CASE_							,  SCREAMING_SNAKE_CASE_	):
      raise ValueError('''Input series is not valid, valid series - [2, 4, 6]'''	)
   if len(SCREAMING_SNAKE_CASE_	) == 0:
      raise ValueError('''Input list must be a non empty list'''	)
   _UpperCAmelCase											=      0
   for val in series:
      answer += 1 / val
   return len(SCREAMING_SNAKE_CASE_	) / answer


if __name__ == "__main__":
   import doctest

   doctest.testmod()