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: 8, 9, ['6753', 'Y', 'v', '1365', '1033', 'l', 'A', '203', 'J', '8391', 'i', '1813', 'V', 'D', 'S', '4981', 'o']
Example Output: 203

Example Input: 8, 14, ['i', '2929', '9353', 'T', '5451', 'n', 'y', '2861', 's', 'G', '7717', '3833', '3753', 'u', 'E', 'T', 'I']
Example Output: 18164

Example Input: 8, 19, ['R', 'g', 'H', '9355', '9433', '8791', '8779', 'l', 'O', '6787', 'f', 'U', '2007', 'N', '5253', '5893', '3941', '7039', 'W', 't', 'e', 'm', '3871', 'M', 'W', 'J', '2763']
Example Output:
30920