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# 23_new - DiscGQ02 gilbert(55035 This print-out should have...

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DiscGQ02 – gilbert – (55035) 1 This print-out should have 4 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine whether the series 1 + 3 + 9 + 27 + · · · is convergent or divergent, and if convergent, find its sum. 1. convergent with sum = 2 9 2. divergent correct 3. convergent with sum = 2 4. convergent with sum = 9 2 5. convergent with sum = 1 2 Explanation: The series 1 + 3 + 9 + 27 + · · · = A R N −1 N =1 is an infinite geometric series in which A = 1 and R = 3. But such a series is A (i) convergent with sum 1 R when |R| < 1, (ii) divergent when |R| ≥ 1 . Thus the given series is divergent . and the series 11 B = F (N) . N = 6 1. A < B 2. A > B correct 3. A = B Explanation: In the figure A 6 A 7 A 8 A 9 . . . 5 6 7 8 9 the bold line is the graph of F on [5, ∞) and the areas of the rectangles the terms in the series A N , A N = F (N) . N

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23_new - DiscGQ02 gilbert(55035 This print-out should have...

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