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: 1, 5, ['O', '4521', 'w', '6745', 'W', '7743', '4113', '7179', '9751', '2365', '9161', 'j', '1339', '6927']
Example Output: 11266

Example Input: 8, 9, ['c', '6341', 'e', 'D', 'D', '613', 'P', 'M', '5539', '1857', '5829', '4147', 'x', '135', 'V', '1649', 'u', 'i', 'x']
Example Output:
5539