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, 19, ['5801', 'N', '5975', 'S', '5451', 'q', '8159', '8477', 'i', 'S', '4009', '9569', '8217', '1105', 'm', 'f', '7415', '6417', '153', '9735', '4547', 'r', '8371', '7553', 'w', 'A', '8139']