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, 10, ['143', '3769', '197', '3281', '1839', '8009', 'J', '1019', 'Z', 'y', 'M', 'w', '827', '3603', 'r', '6401', '1039']
Example Output: 18114

Example Input: 9, 9, ['8633', 'O', 'N', '3323', '1975', '8707', 'c', 'm', '8357', 'A', 'n', '8931', '9021', 'i']
Example Output: 8357

Example Input: 2, 15, ['2361', 'h', '7485', 'v', '5801', '2405', 'D', 'n', '4575', 'L', 'F', 'S', '4743', 'K', 'U', '4277', 'f', 'e']
Example Output:
25009