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, ['9615', '7859', 'D', 'J', '1471']
Example Output: 9330

Example Input: 13, 19, ['5529', 'd', 'W', 'b', 'I', '65', '9995', '6331', '9373', 'V', '8389', 'E', '7455', '105', 'W', 'r', '7733', '7607', 'L', '5553', 'e']
Example Output: 22900

Example Input: 2, 3, ['9377', '921', '3717', 'R', '5481', 'j', '7831', '9331']
Example Output:
4638