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, 20, ['N', '3757', '4835', '557', 'n', '3381', '3229', '9715', 'O', 'J', '5215', 'Q', '7867', 'W', '5159', '1571', '2911', '8907', 'J', 'b']
Example Output: 57104

Example Input: 3, 4, ['1809', '1127', 'm', '3137']
Example Output: 3137

Example Input: 9, 15, ['2935', '1415', '1009', 'N', '127', '6773', '1945', 'F', '827', '6839', 'e', 'B', '4287', '319', '1243']
Example Output:
13515