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, ['3651', '6881', '3701', 'M', '8543', '5995', 'q', 'A', 'S', '745']
Example Output: 25120

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

Example Input: 10, 25, ['4327', 'I', '2757', 'w', '4035', 'B', 'M', '4521', '4977', 'r', '5117', 'h', 'i', '2739', 'r', 'a', '5473', 'g', 'j', 'V', 'm', '2229', '295', 'o', '1839', 'F']
Example Output:
17692