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: 4, 10, ['B', 'b', '6741', '9121', 'N', '2871', 'Z', '1685', '995', '8681', '8591', 'z', '7423', '8661', 'R', 'b', 'g', 'Z', '5679', '4217', 'h', '8497', '3261', '6891', '2145', 'Y']
Example Output: 23353

Example Input: 3, 10, ['q', 'B', 'W', 'm', 'J', '7869', 'c', '1913', 'z', '7737', '5101', 'P', '4349', 'Z']
Example Output:
17519