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, 5, ['9153', 'S', '605', '2951', 'I', 'o', '4995', '2895']
Example Output: 3556

Example Input: 3, 5, ['i', 'e', '6583', '313', '5511']
Example Output: 12407

Example Input: 1, 1, ['1431', '2685', '3781']
Example Output:
1431