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: 4, 25, ['5003', '1565', '5397', '415', '6045', '9119', '3383', '5449', 'v', 'C', 'J', 'w', '7791', 'F', 'O', '8827', '7171', '2709', 'f', 'W', 'P', '5175', 'D', '135', 'W', '7021', 'T', 's', '7949']
Example Output: 56219

Example Input: 6, 12, ['q', '8055', '5233', '5529', 'T', 'h', 'w', 'w', '9449', 'W', '7903', 'b', '6925']
Example Output: 17352

Example Input: 1, 3, ['9917', 'a', '4859', '7973', '1503', 'Z', 'a']
Example Output:
14776