



def 						_lowerCAmelCase    (					__lowerCamelCase :  float		,						__lowerCamelCase :  float		,						__lowerCamelCase :  int  ):



 """simple docstring"""





 __SCREAMING_SNAKE_CASE							:     Optional[int]							=						[1 / first_term]
 __SCREAMING_SNAKE_CASE							:     int							=						1 / first_term
 for _ in range(number_of_terms - 1  ):
  first_term += common_difference
  arithmetic_progression.append(__lowerCamelCase  )
 __SCREAMING_SNAKE_CASE							:     Optional[int]							=						[1 / step for step in arithmetic_progression]
 return sum(__lowerCamelCase  )


if __name__ == "__main__":
      import doctest

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








'''simple docstring'''






from __future__ import annotations







def 		SCREAMING_SNAKE_CASE__					(							_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ):
		if len(_SCREAMING_SNAKE_CASE  ) == 0:
				raise ValueError('''find_min() arg is an empty sequence'''  )
		if (
		    left >= len(_SCREAMING_SNAKE_CASE  )
		    or left < -len(_SCREAMING_SNAKE_CASE  )
		    or right >= len(_SCREAMING_SNAKE_CASE  )
		    or right < -len(_SCREAMING_SNAKE_CASE  )
		):
				raise IndexError('''list index out of range'''  )
		if left == right:
				return nums[left]
		lowerCAmelCase_   :       Dict    							=(left + right) >> 1  # the middle
		lowerCAmelCase_   :       Optional[int]    							=find_min(_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  ,					_SCREAMING_SNAKE_CASE  )  # find min in range[left, mid]
		lowerCAmelCase_   :       Any    							=find_min(_SCREAMING_SNAKE_CASE  ,					mid + 1  ,					_SCREAMING_SNAKE_CASE  )  # find min in range[mid + 1, right]

		return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
							import doctest

							doctest.testmod(verbose=True)






