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, ['Y', 'X', 'r', '439', 'D', 'H', '1903']
Example Output: 439

Example Input: 2, 2, ['9797', '5585', '1849', '4485', '9225']
Example Output: 5585

Example Input: 4, 7, ['2045', '3335', '6053', 'P', '565', '2395', 'b', '2177', '3657', 'v', 'f', '2533', '8503', '5663', 'Y', '4659', '2123', 'T']
Example Output:
2960