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, 9, ['9557', '1661', 'E', '5173', 'o', '4963', '2811', '5471', '3853']
Example Output: 22271

Example Input: 7, 12, ['K', '5995', '5183', '67', '563', '9143', 'M', 'H', '2923', '1825', 'y', '373', 'm', 'w', 'x']
Example Output: 5121

Example Input: 20, 21, ['B', '4745', '5299', '1533', '8215', '3715', 'y', 'g', '6227', 'y', '7643', 'M', 'B', 's', 'P', '2485', '9277', 'k', '2699', '1785', 'S', '6363', 'r', '1959', '2451']
Example Output:
1785