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, ['743', '3417', '5979', 'J', 'f', '4707', 'k', 'i', '2167', 'V', 'g']
Example Output: 14103

Example Input: 3, 4, ['2425', 'J', 'x', '8829', 't', '7927', 'R', 'J', '1599', '3149']
Example Output: 8829

Example Input: 14, 19, ['e', 'Q', 'K', '3771', '6659', '9783', 'r', 'B', '8325', 'C', 'K', 'B', '7857', 'm', 'B', 'Q', '2987', '6517', 'a', '4749', 'R', '1117', '9643']
Example Output:
9504