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: 1, 9, ['6869', '4103', 'S', 'k', '6745', 'n', 'x', '7657', 'F', 'd', '1953']
Example Output: 25374

Example Input: 11, 15, ['W', '8193', '2581', 'f', 'j', '5727', 'A', '6177', 'u', '4201', 'T', 'w', 'C', 'u', '7973', 'd', 'c']
Example Output: 7973

Example Input: 5, 6, ['9393', '6431', 'g', 'P', '2643', '8665', 'r', 'H', '973', '6665', 'V', '6141', 'R', 'J', 'm']
Example Output:
11308