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, 7, ['J', 'l', '9145', '5805', '4377', '2851', '8781', '7353', '145']
Example Output: 30959

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

Example Input: 3, 11, ['8307', '1391', '5153', '6195', 'l', '159', '7179', '8877', '3033', 'd', '9483', '5815', 'D', 'I', '4557', '9835', 'G']
Example Output:
40079