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: 2, 7, ['o', '3377', 'x', '9385', 'z', '9963', 'S', 'h', 'l', '1525', 'k']
Example Output: 22725

Example Input: 1, 1, ['x', 'g', 'X', 'j', 'k', '9821', 'n', 'd', '1709', 'r']
Example Output: 0

Example Input: 8, 11, ['i', '6215', '6367', 'U', 'D', '5425', '8967', 'w', '9677', 'J', '495', 'N', 'P']
Example Output:
10172