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, 4, ['261', '6237', '3809', '1857']
Example Output: 12164

Example Input: 4, 8, ['3753', 'y', '417', 'B', 'g', 'D', 'L', '6175']
Example Output: 6175

Example Input: 2, 10, ['907', '3413', 'y', 'Y', 'y', '9671', '6631', 'g', '8803', '3127', 'k', 'Y', '413', '3871', '909', 'G', '4431', '6489', '7291', 'J', 'W', '6423', '641', 'G', '2545', '4471', '3717', '2671', '561']
Example Output:
31645