a. Suppose that 0 < q < p and that n = + O(np). Show that

a. Suppose that 0 < q < p and that αn = α + O(n−p). Show that αn = α + O(n−q).
b. Make a table listing 1/n, 1/n2, 1/n3, and 1/n4 for n = 5, 10, 100, and 1000, and discuss the varying rates of convergence of these sequences as n becomes large.