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: 7, 15, ['1769', 'c', '7895', '8687', '985', '7559', '1109', 'X', 'z', '2309', 'D', 'P', '8655', 'I', 'u', 'z', '9639', '83', '7631']
Example Output: 12073

Example Input: 4, 5, ['1427', '7597', '765', 't', '7057', 'f', 'B', 'k']
Example Output: 7057

Example Input: 15, 21, ['6457', 'j', 'Y', 'O', '5119', '1515', '255', 'y', 'k', 'r', 'v', 'j', 'c', '313', '8243', 'T', 'i', '5379', 'q', 'S', '4769', 'p', 'w', '1705', '3563']
Example Output:
18391