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, 8, ['r', 'H', 'K', 'K', '7307', 'i', '9381', '4175']
Example Output: 20863

Example Input: 1, 3, ['F', 'N', 'N', 'r', 'X', 'R', '3477', 'T', 'z', 'v', 'B', 'Q']
Example Output: 0

Example Input: 4, 10, ['B', 'b', '6741', '9121', 'N', '2871', 'Z', '1685', '995', '8681', '8591', 'z', '7423', '8661', 'R', 'b', 'g', 'Z', '5679', '4217', 'h', '8497', '3261', '6891', '2145', 'Y']
Example Output:
23353