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: 1, 6, ['237', 'x', 'Q', 'J', '4629', 'q', '2831', 'i', 'm']
Example Output: 4866

Example Input: 1, 14, ['9503', '5983', '143', 'j', '9227', 'g', 'X', '5995', '6623', 'k', 'q', '1047', '2815', '569', 's', 'D', '4045', 'G', '9707', '6707', '7953', 'R']
Example Output: 41905

Example Input: 5, 9, ['n', 'y', 'z', '6911', 'U', 'd', '3683', '3357', 'O', 'J', '1163']
Example Output:
7040