In this task, you are given inputs i,j, and A, where i and j are integers and A is a list. You need to return the sum of all the numerical elements in the list A between the positions i and j (including positions i and j). Return 0 if no numerical element is present in the list between the given ranges. i and j will be non-negative, and will always have a value less than the length of A. i will always be less than j.

Example Input: 3, 4, ['2977', 'i', 'l', 'r', '8835', '7697', 'p', '1685', 'h', 'N', 'Z', '8661', '6003', '7007', 'D', 'C']
Example Output: 0

Example Input: 16, 18, ['o', '3669', 'M', 'M', 'R', 'r', 'o', 'P', 'q', '9939', '1807', 'F', 'J', 'a', '7773', 'I', 'A', '475', 'W', 'E', '417']
Example Output: 475

Example Input: 2, 4, ['L', '8053', '8121', 'J', 'H', '7591', 'U', 'm']
Example Output:
16174