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: 1, 2, ['t', '9343', 'g']
Example Output: 9343

Example Input: 10, 21, ['K', '8439', '7235', 'M', '5943', '831', '6943', 'D', '4405', '6019', '9399', '5733', '3681', 'R', 'o', '3347', 'N', '1811', '9859', '5809', 'd', 'k', '9543', 'B']
Example Output:
45658