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, 8, ['r', 'H', 'K', 'K', '7307', 'i', '9381', '4175']
Example Output: 20863

Example Input: 10, 11, ['J', '5319', '1625', 'z', '275', 'B', '6901', 'b', 'X', '8669', '2307', '3117', 'K']
Example Output: 10976

Example Input: 1, 17, ['5979', '4799', 'v', 'V', 'd', 'O', '5225', 'w', '2509', '9307', 'U', 'B', '5309', 'j', '4437', 'o', 'k', 'T', 'D', 'g', '369', 'A']
Example Output:
37565