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, 7, ['J', 'l', '9145', '5805', '4377', '2851', '8781', '7353', '145']
Example Output: 30959

Example Input: 3, 4, ['u', '5041', 'E', 'U', 'a', 'd']
Example Output: 0

Example Input: 1, 5, ['q', '2269', '6477', '3473', 'Z', '9785', '6957', 'k', 'q', 's', '3305', '1201', 'X', '8387']
Example Output:
12219