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: 3, 4, ['3949', '5315', 'G', 's', 'v', 'm', '7833', 'E', 'j']
Example Output: 0

Example Input: 1, 2, ['E', 'z']
Example Output: 0

Example Input: 5, 13, ['W', '1605', 'a', 'C', 'u', '5259', 'M', '883', '1699', '2353', '9563', '203', 'Q', 'j']
Example Output:
19960