Suppose that you have a dynamic array. If the array has room available when you want to append an element, the cost is just O(1). But if the array is full when you want to append an element, the cost will be O(1) plus a cost to expand the array. Expanding the array means that you will double its current size. It also means that you will have to copy each element from the old array into the new (expanded) array. A copy operation costs O(1) per element copied. Using the aggregate method, show that the amortized cost of n append operations is O(1).