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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. |
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