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, 4, ['2107', 'l', '7551', '4907']
Example Output: 4907

Example Input: 10, 11, ['J', '5319', '1625', 'z', '275', 'B', '6901', 'b', 'X', '8669', '2307', '3117', 'K']
Example Output: 10976

Example Input: 1, 3, ['e', '51', '3919']
Example Output:
3970