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: 1, 1, ['x', 'g', 'X', 'j', 'k', '9821', 'n', 'd', '1709', 'r']
Example Output: 0

Example Input: 4, 4, ['t', 'Z', '8689', 'I', '5589', 'H', 'Z']
Example Output: 0

Example Input: 4, 8, ['w', 'T', '8793', '6449', 'X', 'v', 'N', '1813', 'Y', 'N', 'D', 'M', '4033']
Example Output:
8262