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, 10, ['2095', '7189', 'j', 'i', '6105', 'f', 'I', 'z', '7903', '7165']
Example Output: 15068

Example Input: 3, 18, ['h', 'x', '371', 'i', '8545', '7767', '5033', '1041', 'A', '4643', 'L', '187', '5017', 'x', 'R', '7891', '3919', '9721', '8625', '5817', 'D', '4825', 'S']
Example Output: 54135

Example Input: 2, 3, ['2201', 'n', '8725']
Example Output:
8725