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: 8, 12, ['i', '35', 'v', 'G', 'o', '5861', '8371', 'P', '1895', '6183', '8025', '2455', '4763', '409', 'e', 'A', '9029', 'a', 'I', '2761', '5481', 'f', '3413', '803', 'W', 'A', '8781']
Example Output: 18558

Example Input: 3, 7, ['k', 'm', 'W', '641', 'X', 'B', '897']
Example Output: 1538

Example Input: 1, 2, ['J', 's', 'T', '5851']
Example Output:
0