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, 4, ['261', '6237', '3809', '1857']
Example Output: 12164

Example Input: 13, 14, ['6693', 'J', '2765', 'P', 'h', '755', 'z', '7483', 'W', '6895', '1293', '3479', 'Y', '1667', '9635']
Example Output: 1667

Example Input: 4, 8, ['5311', 'y', '5675', '4639', '9681', '8063', '8105', 'g', '1415', 'l', '8721', 'o', '8171', 'h', '5863', '9961', 'l', '7', 'K']
Example Output:
30488