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, 10, ['2797', 'm', '439', '5677', '6719', '1587', 'I', 'I', 'w', '8483', '7341', '341', 'H', 'K', '7727', '4467', 'L']
Example Output: 22905

Example Input: 2, 5, ['W', 'A', 'm', 'w', 'r', '9705', '1729', 'U', '2171', 'Q', 'Y', 'P', 'O']
Example Output: 0

Example Input: 3, 7, ['c', '1457', 'z', 'p', 'F', '4043', '2049']
Example Output:
6092