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: 8, 9, ['3587', '5903', 'B', '9671', 's', 'A', '7259', '6961', '2601', '9719']
Example Output: 9562

Example Input: 1, 15, ['t', '77', '6593', '3683', '5673', '9391', 'Y', 'A', '3273', '379', '6569', 'l', 'u', '8633', 'M', '8587', '3127', '5885', '4083']
Example Output: 44271

Example Input: 3, 4, ['6919', 'q', 'b', '1119', 'H']
Example Output:
1119