Show your work (6 points) How many elements can be represented using a complete binary tree having: depth 0, depth 1, depth 2, depth 3, depth 4. In a complete binary tree, each node has exactly two children. (3 points) Using induction, show that the sum of the sequence S = 1 + 2 + 4 + 8 + 16 + 2In is 2n+1 1. The first term corresponds to the value of n = 0, the second term corresponds to the value of n = 1, and so on. Relate it to your solution in Problem 2a. Explain the meaning of this sum in terms of tree problem given in problem 2a. Note that n is the same as the depth of the tree in problem 2a. (3 points)