






"""simple docstring"""





from __future__ import annotations






def     A(  snake_case_						,       snake_case_						,       snake_case_						,       ):
       """simple docstring"""





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














"""simple docstring"""





def     A(  snake_case_		):
       """simple docstring"""





       if not isinstance(snake_case_						,       snake_case_		):
              raise ValueError("Input series is not valid, valid series - [1, 2/3, 2]"		)
       if len(snake_case_		) == 0:
              raise ValueError("Input list must be a non empty list"		)
       if len(snake_case_		) == 1 and series[0] != 0:
              return True
       lowercase__:    str        =      []
       lowercase__:    Optional[int]        =      len(snake_case_		)
       for i in range(0						,       snake_case_		):
              if series[i] == 0:
                     raise ValueError("Input series cannot have 0 as an element"		)
              rec_series.append(1 / series[i]		)
       lowercase__:    Optional[int]        =      rec_series[1] - rec_series[0]
       for index in range(2						,       snake_case_		):
              if rec_series[index] - rec_series[index - 1] != common_diff:
                     return False
       return True






def     A(  snake_case_		):
       """simple docstring"""





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


if __name__ == "__main__":
  import doctest

  doctest.testmod()






