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: 12, 15, ['I', 'H', '3483', '6289', 'X', '5705', '7707', 'x', 'J', 'c', '5161', '9653', '3949', 'l', 'b', 'C', 's', '17', 'a', '4231', 't']
Example Output: 13602

Example Input: 3, 22, ['k', '427', 'x', '9695', 'a', '2243', '329', 'F', 'n', '6253', '4873', 'f', 'z', 'R', 'b', '4351', 'b', 'i', 'g', '6937', 'I', 'k', 'f']
Example Output: 34681

Example Input: 1, 11, ['O', '9557', '841', '4581', 'k', 'U', 'R', 'k', 'S', 'q', '4737']
Example Output:
19716