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, 1, ['x', 'g', 'X', 'j', 'k', '9821', 'n', 'd', '1709', 'r']
Example Output: 0

Example Input: 2, 9, ['7111', '835', 'W', '6975', '4459', 'B', 'B', 'Z', 'o']
Example Output: 12269

Example Input: 7, 14, ['6627', '8351', '8023', 'T', 'Q', 't', '1471', '9049', 'Y', '1155', '8067', 'D', '9481', 'V', 'P', '3229', '3349', 'o', '3321', '2903', '205', 'R', '2143', '1847']
Example Output:
29223