




'''simple docstring'''



def       _UpperCamelCase			(_lowerCamelCase				:  list[int] ,						_lowerCamelCase				:  int						)-> bool:




     '''simple docstring'''





     __snake_case            =	len(_lowerCamelCase						)
     __snake_case            =	[[False] * (required_sum + 1) for _ in range(arr_len + 1						)]

     # for each arr value, a sum of zero(0) can be formed by not taking any element
     # hence True/1
     for i in range(arr_len + 1						):
          __snake_case            =	True

     # sum is not zero and set is empty then false
     for i in range(1 ,						required_sum + 1						):
          __snake_case            =	False

     for i in range(1 ,						arr_len + 1						):
          for j in range(1 ,						required_sum + 1						):
               if arr[i - 1] > j:
                    __snake_case            =	subset[i - 1][j]
               if arr[i - 1] <= j:
                    __snake_case            =	subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

     return subset[arr_len][required_sum]


if __name__ == "__main__":
     import doctest

     doctest.testmod()












'''simple docstring'''



def       _UpperCamelCase			(_lowerCamelCase				:  int ,						_lowerCamelCase				:  int ,						_lowerCamelCase				:  int						)-> float:




     '''simple docstring'''





     __snake_case            =	(num_of_terms / 2) * (2 * first_term + (num_of_terms - 1) * common_diff)
     # formula for sum of series
     return total







def       _UpperCamelCase			()-> str:




     '''simple docstring'''





     print(sum_of_series(1 ,						1 ,						10						)						)


if __name__ == "__main__":
     import doctest

     doctest.testmod()






