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: 1, 6, ['7349', 'S', '4839', 'R', '4443', '7569', '7307']
Example Output: 24200

Example Input: 1, 9, ['6607', '6185', 'X', 'd', 'T', 't', 'Y', 'p', '2789', 'a', '7365', 'k', 'n', '1853', 'x', 'F', '5523', '2827', '1441', 'F', 'c', 'i', 'n', 'h', '3633']
Example Output: 15581

Example Input: 6, 12, ['5003', '8743', '2899', '8359', '8007', 't', 'x', '6077', '8473', '7423', '1549', '2045', 'O', '5677']
Example Output:
25567