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, 3, ['e', '1703', 'x', 'U', '873']
Example Output: 1703

Example Input: 1, 3, ['7641', '5147', '995', 's', '6697']
Example Output: 13783

Example Input: 2, 5, ['9567', 't', '4169', 'b', '4569', 'b', '7217', '5857', 'g', '7079', '3555', 'a', 'k']
Example Output:
8738