
import numpy as np





def    _a (						lowerCamelCase							):
 lowerCamelCase		:     List[str]          =				np.exp(lowerCamelCase							)

 # Add up the all the exponentials
 lowerCamelCase		:     str          =				np.sum(lowerCamelCase							)

 # Divide every exponent by the sum of all exponents
 lowerCamelCase		:     Union[str, Any]          =				exponent_vector / sum_of_exponents

 return softmax_vector


if __name__ == "__main__":
      print(softmax((0,)))






def    _a (						lowerCamelCase,     lowerCamelCase,     lowerCamelCase							):
 lowerCamelCase		:     Optional[int]          =				[1 / first_term]
 lowerCamelCase		:     Any          =				1 / first_term
 for _ in range(number_of_terms - 1							):
  first_term += common_difference
  arithmetic_progression.append(lowerCamelCase							)
 lowerCamelCase		:     Optional[Any]          =				[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))




