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: 10, 17, ['479', '9493', '9061', '5585', 's', '9653', '5741', '7451', '2141', '9547', 'r', 'Z', '8915', '8289', '9281', '561', 'J', '3029', '3595', '7279', '7641']
Example Output: 36593

Example Input: 6, 7, ['6997', '3987', '2463', 'm', 'W', 'R', 'a', 'U', 's', 'Y', 'X', '4193', '343', 'Y', '4277', 'n', 'W']
Example Output: 0

Example Input: 5, 6, ['i', 'i', 'J', 'O', '4571', 'o', '2073', '87', 'x', '9937', '9917', '4283', 'S']
Example Output:
4571