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: 2, 8, ['4225', 'k', '4097', '4459', '8125', '431', '495', 'Z']
Example Output: 17607

Example Input: 1, 4, ['261', '6237', '3809', '1857']
Example Output: 12164

Example Input: 2, 22, ['9203', '8285', '3553', '8607', 'j', 'z', 'l', '755', '7119', '5781', '3159', '4171', '6675', '429', 'g', 'S', '2481', 'r', 'l', 'Y', 'N', '133', '4675', 'V', '8505', '2997', 'g']
Example Output:
51148