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: 5, 9, ['1523', 'C', 'd', 'I', '6913', '5553', '2769', '767', 'v', '231', 'I', 'p', '9033', 'H', '2007', 'g', '5837', 'Z']
Example Output: 16002

Example Input: 3, 4, ['4845', '7313', 'P', 'A', '2285', 'C', 't']
Example Output: 0

Example Input: 3, 4, ['J', '1447', 'l', '5611', 'k', '1273']
Example Output:
5611