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: 5, 8, ['j', '1099', 'J', 'l', 'E', '6559', '6181', '4441']
Example Output: 17181

Example Input: 6, 9, ['J', '5177', 'm', '7413', 'T', 'N', '5153', 'S', '8145']
Example Output: 13298

Example Input: 4, 6, ['T', 'm', 'P', '3561', 'X', '5647', 'g', '2039']
Example Output:
9208