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: 5, 13, ['8179', '2435', 'w', '6965', '2003', 'c', '2091', 'w', '225', 's', 'k', '4281', '1931', '3351', 'o', 'f', 'Y', 'm', '8223', 'X', 'H', 'X']
Example Output: 10531

Example Input: 1, 7, ['v', '8881', '2711', '7569', 'C', '6117', '1569', '1257', 'h', '5407']
Example Output: 26847

Example Input: 9, 20, ['C', '4801', '2673', 'D', 'q', 'z', '5473', 'u', '5465', 'o', 'G', '3191', 'I', 'i', '9101', 'm', 'w', '1855', 'X', '3341']
Example Output:
22953