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, 6, ['g', '8871', 'q', '597', '8871', '277', 'f', 'e', '2779']
Example Output: 9745

Example Input: 2, 9, ['F', '7137', '6127', 'q', '6637', '1423', 'w', '4175', '8971', '3999', '193']
Example Output: 34470

Example Input: 3, 3, ['x', 'A', 'i', '5267', 'S', 'Y']
Example Output:
0