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.

1, 7, ['J', 'l', '9145', '5805', '4377', '2851', '8781', '7353', '145']
30959

6, 8, ['s', 'X', 'a', 'L', 'N', 'J', '1893', '4909', '349', '7679', '4479', 'i', '7345']
6802

2, 3, ['4673', 'E', '2443']

2443