13) Euler's Constant: In MATH 648 we will be able to show that Prove that {an} converges. Note: y = lim an is called Euler's constant. It is not known whether Euler's constant is n +1 0. f) Based on the estimate in e) explain why the Harmonic series _ : diverges to infinity. 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 g) Suppose that we wrote a computer routine to calculate (In(k + 1) - In(k)) = In(n + 1). SKo = 1+7+3 + ...+ Ko k = 1 by simply adding one term at a time where Ko is some fixed natural number. Suppose that c) Use part (b) to show that we wanted to choose Ko large enough so that SKo > 106 0