Homework12 - 1 36-1 49-1 64 ·· converge or diverge Explain your answer CONTINUE TO THE NEXT PAGE Math 1120 Fall 2011 Homework 12 — due 11/17

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Math 1120 Homework 12 Due 11/17 or 11/18, 2011 Name: GRADES Book questions / 8 Presentation questions / 45 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 — 10.5: 4, 12, 16, 24 10.6: 6, 18, 39, 40 Presentation questions 1. [10 points] (10.5: 28) Does the series s n =1 (ln n ) n n n converge or diverge? Explain your answer. CONTINUE TO THE NEXT PAGE.
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Math 1120, Fall 2011 Homework 12 — due 11/17 or 11/18 2 2. [10 points] (10.6: 48) Does the series 1 + 1 4 - 1 9 - 1 16 + 1 25 +
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Unformatted text preview: 1 36-1 49-1 64 + ··· converge or diverge? Explain your answer. CONTINUE TO THE NEXT PAGE. Math 1120, Fall 2011 Homework 12 — due 11/17 or 11/18 3 3. [10 points] (10.6: 58) Approximate the sum ∞ s n =0 (-1) n 1 n ! within an error of magni-tude less than 5 × 10-6 . ( We will see in Section 10.9 that the sum is e-1 .) CONTINUE TO THE NEXT PAGE. Math 1120, Fall 2011 Homework 12 — due 11/17 or 11/18 4 4. [15 points] (10.6: 62) Show that the sum of the Frst 2 n terms of the series 1-1 2 + 1 2-1 3 + 1 3-1 4 + 1 4-1 5 + 1 5-1 6 + ··· is the same as the sum of the Frst n terms of the series 1 1 · 2 + 1 2 · 3 + 1 3 · 4 + 1 4 · 5 + 1 5 · 6 + ··· . Do these sums converge? What is the sum of the Frst 2 n + 1 terms of the Frst series? If the sums converge, what is their sum? THIS IS THE LAST PAGE....
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This note was uploaded on 10/31/2011 for the course MATH 1120 at Cornell University (Engineering School).

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Homework12 - 1 36-1 49-1 64 ·· converge or diverge Explain your answer CONTINUE TO THE NEXT PAGE Math 1120 Fall 2011 Homework 12 — due 11/17

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