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: 6, 7, ['6261', 'l', 'T', 't', 'X', 'G', 'Y', 'f']
Example Output: 0

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: 5, 15, ['855', 'c', 'L', '8499', '3413', 'i', '3789', '155', '9103', 'y', '2275', '1223', '9211', '1875', '6603', '1759', 'H', '7939', 'F', '4101']
Example Output:
37647