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, 19, ['u', 'x', '1103', 'K', 'N', 'o', '1943', 'Z', 'r', 'B', 'N', 'e', '7289', 'S', '325', 'G', 'x', 'D', '9005', 'y', '1729', '961', '4621', 'D', 'u', '1235']
Example Output: 19665

Example Input: 5, 10, ['P', '5679', 'o', '293', '9307', '5985', '7593', '5635', 'B', 'I']
Example Output:
28520