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, 2, ['9797', '5585', '1849', '4485', '9225']
Example Output: 5585

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: 7, 14, ['5759', '291', 'd', 'B', '1537', '749', '4169', 'M', '7299', 'X', 'r', '5445', '6755', 'a', 'j', '7907', 'R']
Example Output:
23668