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: 3, 16, ['1661', '2609', '7987', '619', '6765', '5249', '1377', '8971', 'J', 'o', '4803', 'O', '699', '4415', 'V', '1813', 'j', 'm', 'L']
Example Output: 42698

Example Input: 3, 7, ['1687', '1929', '3189', '3277', 'L', 'b', 'x', '3181', 'C', 'w', 'A', 't', 'I', '3421']
Example Output: 6466

Example Input: 7, 18, ['5653', 'q', '4589', 'P', 'A', 'H', 'L', 'u', '5567', 'j', '1677', 's', '4719', '9123', '7013', '9329', 'z', '5133', 'e', 'J', '7849', '9017', '9', '2583', 'b']
Example Output:
42561