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, 6, ['237', 'x', 'Q', 'J', '4629', 'q', '2831', 'i', 'm']
Example Output: 4866

Example Input: 2, 16, ['e', 'Q', '4017', '1999', '2413', 'v', '4911', 'N', 'x', '3475', '2179', 'o', 'a', '6361', '1723', '6273']
Example Output: 33351

Example Input: 9, 12, ['1239', '9839', '8285', 'R', '3721', '8317', 'L', 'I', 'M', 'j', '3855', 'J']
Example Output:
3855