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, ['1595', '1523', '157', 'I', '3929', '6313', 'H', 'f', 'e', '93', '5625', 'b', 'J', 'b', '1185', '1505', 'I', 'y', '4043']
Example Output: 6313

Example Input: 2, 8, ['6901', '3901', '5101', '4297', '1099', 'q', 'z', '6615', 'z', '6859']
Example Output: 21013

Example Input: 2, 6, ['8375', 'b', 'j', 'G', '4899', 'y']
Example Output:
4899