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, ['P', 'V', '5567', 'm', 'V', '9533', '2381', '1095', '835', 'B', 'z', 'J', 'H', 't', 'b', 'z', 'e']
Example Output: 1930

Example Input: 3, 4, ['6203', 'g', '471', 'j', 'o', '9679', 'M', '5459', 'y', '1929', '1649', 'C']
Example Output: 471

Example Input: 4, 4, ['679', 'k', '7427', 'R', '1851', '1399', 'S', 'S']
Example Output:
0