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, 7, ['E', 'e', '5585', 'g', '4971', '8891', '811', 'l', '527', '4299', 'b', 'N', '5079', 'j', '5555', '4789']
Example Output: 20258

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

Example Input: 3, 5, ['2673', 'B', '6499', '8181', '5217']
Example Output:
19897