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, 3, ['Z', 'X', 't']
Example Output: 0

Example Input: 2, 3, ['f', 'C', 'f', 'V', 't', 'x']
Example Output: 0

Example Input: 4, 6, ['w', '8169', '4999', '9015', '1973', '1005']
Example Output:
11993