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, 11, ['L', 'Z', '4501', '4131', 'a', '8057', 'K', 'P', '4713', '8889', 'b', '3927', 'k', '6005', 'T', 'w', 'S', '3963', '2727']
Example Output: 8889

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

Example Input: 5, 14, ['r', '5851', '5957', '1951', '9761', '6805', '2323', 'J', '703', '9479', '6653', 'L', '513', 'A', 'v', '4273', '391', 'b']
Example Output:
36237