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: 11, 19, ['Y', 'r', 't', '2931', '9519', '1071', '2417', 'p', 'F', '7509', 'l', '3451', '1907', 'z', 'E', 'n', '1251', 'k', 'p']
Example Output: 6609

Example Input: 12, 18, ['9047', '1191', '7027', 'b', '1877', 'n', '337', 'n', 'o', '9007', 'd', 'F', '4929', '2707', 'B', 'y', 'o', '2859', '1609', 'N', 'w', 'H']
Example Output: 10495

Example Input: 7, 8, ['3657', '9747', 'P', '6265', '8705', '8749', '3875', '3911']
Example Output:
7786