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: 3, 16, ['1661', '2609', '7987', '619', '6765', '5249', '1377', '8971', 'J', 'o', '4803', 'O', '699', '4415', 'V', '1813', 'j', 'm', 'L']
Example Output: 42698

Example Input: 2, 15, ['4175', '6415', 'U', '8883', 'J', '5843', '3923', '8991', 'P', 'm', 'S', 'T', '5819', 'q', '7405']
Example Output: 47279

Example Input: 1, 3, ['N', 'm', '5963']
Example Output:
5963