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: 2, 5, ['4487', '3761', '159', '7459', '6781', '2403', 'S', '3079', '7161']
Example Output: 18160

Example Input: 5, 9, ['125', 'A', 'E', 'X', 'j', '319', 'm', '7037', 'g', 'D', 'g', '6737', 'z', '5249']
Example Output: 7356

Example Input: 1, 4, ['9943', 'V', 'w', '5495', '8739', 'V', 'm', '7083']
Example Output:
15438