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: 3, 8, ['3071', 'N', '2157', 'g', 'l', '9317', '8639', '2519', '6257']
Example Output: 22632

Example Input: 2, 3, ['f', 'C', 'f', 'V', 't', 'x']
Example Output: 0

Example Input: 1, 3, ['2725', 'v', '8879', '6213', 'c']
Example Output:
11604