13) Euler's Constant: [32 Marks, 4 for each part] In MATH 648 we will be able to show that 1 n +1 0. for every n E N and hence that {an } is a decreasing sequence. (Note: You do not have to use induction here.) b) Show either directly or by induction that E(In(k + 1) - In(k)) = In(n + 1). K = 1 c) Use part (b) to show that 0 106 Question: Would a modern computer be able to perform enough additions one at a time to calculate 3K0 in one hour? (Choose 1) i) Yes, since modern computers are extremely fast. ii) No. After a billion years you would still not be close. h) Briey explain your answer to part g) above