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, ['2227', '1525', 'g', 'l', 'R']
Example Output: 0

Example Input: 2, 7, ['C', 'C', '9639', '7815', 'N', '1713', '8339', '4237']
Example Output: 27506

Example Input: 9, 23, ['J', '8045', 'r', '4257', 'S', 'E', '677', 'b', 'I', 'h', '3969', 'd', '3095', 'x', '6837', 'j', 'y', '5507', 'C', 'X', 'J', 'q', 'P', 'J']
Example Output:
19408