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: 4, 5, ['677', '5585', 'W', 'J', 'C']
Example Output: 0

Example Input: 5, 12, ['2653', 'A', '4739', '149', 'J', '817', 'n', '9589', '965', '1545', 'r', '9061', '7973', '5769', 'Y', '5889', 'A', 'P', '5789', '9757']
Example Output: 21977

Example Input: 17, 17, ['5309', '5897', 'i', 'k', 'L', 'S', '3535', 't', '6043', '27', 'J', '3605', 'N', 'R', 'j', '9729', 'C', 'D', '1013', 'l', 'w']
Example Output:
0