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: 10, 11, ['A', 'H', 's', '8033', 'M', '7393', '1231', 'T', '5025', '1739', 'q', '4233']
Example Output: 1739

Example Input: 2, 9, ['3707', 'J', 'H', '8907', '597', 'Z', '9725', 'g', 'R']
Example Output: 19229

Example Input: 6, 20, ['1415', 'x', 'g', 'i', '9937', '2681', 'N', 'i', '4953', '8877', '4599', '5547', 'n', 'T', '2289', '2615', '8275', 'X', 't', 'o', '5347', 'S', '2095', 't', 'U']
Example Output:
39836