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: 6, 16, ['P', '8933', '2757', 'y', 'p', '6687', '6903', 'S', 'b', '7221', 'V', 'B', '3633', 'G', '1209', 'J', '641', '1449', 's', 'w', 'C', '5801', 'Y']
Example Output: 25653

Example Input: 2, 9, ['3707', 'J', 'H', '8907', '597', 'Z', '9725', 'g', 'R']
Example Output: 19229

Example Input: 2, 3, ['2045', '5711', 'S', 'm', 'r', '8273', 'f', 'r', 'E']
Example Output:
5711