Proposition E. In the resizing array implementation of Stack (Algorithm 1.1), the average number of array accesses for any sequence of operations starting from an empty data structure is constant in the worst case. Proof sketch: For each push() that causes the array to grow ( say from size N to size 2N), consider the N/2 - 1 push() operations that most recently caused the stack size to grow to k, for k from N/2 + 2 to N. Averaging the 4N array accesses to grow the array with N/2 array accesses (one for each push), we get an average cost of 9 array accesses per operation. Proving that the number of array accesses used by any sequence of M operations is proportional to M is more intricate (see Exercise 1.4.32)

Explain the proposition in detail, also redo the work assuming we are tripling the array. Please use same wording as the proposition.