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: 3, 6, ['w', 'V', '7413', '5027', 's', '7037', 'S', '763', 'D', 'U', 'x', 'l', '9331', 'S', 'k', '8369', 'D', 'A', 'e', 'A', 'r', '5113', '1367', '4197', 'm']
Example Output: 19477

Example Input: 4, 9, ['9557', '1661', 'E', '5173', 'o', '4963', '2811', '5471', '3853']
Example Output: 22271

Example Input: 9, 20, ['5873', '1631', 'k', 'x', 'I', 'r', '9475', 'k', '7211', 'G', '4541', '5683', '4385', '8305', 's', '2143', '997', '3433', '8003', '7029', 'Q', '8839', 'b', 'r']
Example Output:
51730