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: 1, 4, ['2025', '6689', '1227', '3943', 'z', '719', '8941', 'b', 'V', 'w', '5267', '2403', 'N', '5771']
Example Output: 13884

Example Input: 1, 9, ['6869', '4103', 'S', 'k', '6745', 'n', 'x', '7657', 'F', 'd', '1953']
Example Output: 25374

Example Input: 2, 3, ['1485', '8491', '7219', 'h', '2015', '1689', '9869', 'S']
Example Output:
15710