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# homework11 - Math 1120 Fall 2011 Homework 11 — due 11/10...

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Math 1120 Homework 11 Due 11/10 or 11/11, 2011 Name: GRADES Book questions / 8 Presentation questions / 36 Print out these pages. Answer the “presentation questions” in the spaces provided. Include full explanations and write your answers in complete, mathematically and grammatically correct sentences. Your answers will be assessed for style and accuracy; you will be given written feedback on these prob- lems. Write your answers to the “book questions” on separate paper and staple to these pages. They will be assessed only for completeness. Always write neatly and legibly. Book questions — 10.3: 6, 12, 26, 32 10.4: 4, 10, 26, 32 Presentation questions 1. (10.3: 43, adapted ) (a) [8 points] Draw illustrations to show that the partial sums of the harmonic series satisfy the inequalities ln( n + 1) = i n +1 1 1 x dx 1 + 1 2 + · · · + 1 n 1 + i n 1 1 x dx = 1 + ln n. CONTINUE TO THE NEXT PAGE.

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Unformatted text preview: Math 1120, Fall 2011 Homework 11 — due 11/10 or 11/11 2 (b) [8 points] Suppose 13 billion years ago (the day the universe was formed, appar-ently) you start with s 1 = 1 , and you add a new term every second . About how large would the partial sum s n of the harmonic series be on 11/10/2011 (that is, about now), assuming a 365–day year. 2. [10 points] (10.4: 40) Does the series ∞ s n =1 2 n + 3 n 3 n + 4 n converge or diverge? Explain your answer. CONTINUE TO THE NEXT PAGE. Math 1120, Fall 2011 Homework 11 — due 11/10 or 11/11 3 3. [10 points] (10.4: 58) Show that if ∑ a n is a convergent series of nonnegative terms, then ∑ a n 2 converges. ( You many use results from the textbook or from class, provided you state them clearly. ) THIS IS THE LAST PAGE....
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homework11 - Math 1120 Fall 2011 Homework 11 — due 11/10...

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