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: 2, 5, ['W', 'A', 'm', 'w', 'r', '9705', '1729', 'U', '2171', 'Q', 'Y', 'P', 'O']
Example Output: 0

Example Input: 1, 9, ['6869', '4103', 'S', 'k', '6745', 'n', 'x', '7657', 'F', 'd', '1953']
Example Output: 25374

Example Input: 2, 4, ['e', '3055', '9111', '8723', '7841', 'n', '5359', 'q']
Example Output:
20889