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, 8, ['3753', 'y', '417', 'B', 'g', 'D', 'L', '6175']
Example Output: 6175

Example Input: 1, 7, ['u', 'Z', 'j', 'A', 'N', 's', 'h', '7331', '8259']
Example Output: 0

Example Input: 9, 9, ['G', '9137', 'G', '2393', '9383', 'r', '6897', '547', 'W', 'h', 'p', '4557']
Example Output:
0