






"""simple docstring"""





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





       lowercase__:							Optional[Any]         =     [1 / first_term]
       lowercase__:							List[str]         =     1 / first_term
       for _ in range(number_of_terms - 1						):
              first_term += common_difference
              arithmetic_progression.append(snake_case_						)
       lowercase__:							List[str]         =     [1 / step for step in arithmetic_progression]
       return sum(snake_case_						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  print(sum_of_harmonic_progression(1 / 2, 2, 2))













"""simple docstring"""






def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							bool:






       """simple docstring"""




       if not isinstance(SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				):
              raise ValueError('Input series is not valid, valid series - [2, 4, 8]'				)
       if len(SCREAMING_SNAKE_CASE				) == 0:
              raise ValueError('Input list must be a non empty list'				)
       if len(SCREAMING_SNAKE_CASE				) == 1:
              return True
       try:
              _UpperCAmelCase			     =  series[1] / series[0]
              for index in range(len(SCREAMING_SNAKE_CASE				) - 1				):
                     if series[index + 1] / series[index] != common_ratio:
                            return False
       except ZeroDivisionError:
              return False
       return True

def    __lowerCamelCase     (							SCREAMING_SNAKE_CASE				)		->							float:






       """simple docstring"""




       if not isinstance(SCREAMING_SNAKE_CASE,SCREAMING_SNAKE_CASE				):
              raise ValueError('Input series is not valid, valid series - [2, 4, 8]'				)
       if len(SCREAMING_SNAKE_CASE				) == 0:
              raise ValueError('Input list must be a non empty list'				)
       _UpperCAmelCase			     =  1
       for value in series:
              answer *= value
       return pow(SCREAMING_SNAKE_CASE,1 / len(SCREAMING_SNAKE_CASE				)				)


if __name__ == "__main__":
    import doctest

    doctest.testmod()






