Solutions to Homework 6 Problem 2. Since we can compute the limit as (25) Problem 7. By the Cauchy-Schwarz inequality, (26) Both series on the right are convergent, hence the partial sums are bounded so the partial sum on the left is bounded, hence, being a series of non-negative terms, convergent. Problem 12. (a) Since the is strictly decreasing as increases. Thus for (27) It follows that the.
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