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# Let an S1 1 1 n D n . (a) Show that if 0 < a , b, then bn11 2 an11 b 2 a , sn 1 1dbn (b)

ISBN: 9781305270336 484

## Solution for problem 90 Chapter 11.1

Single Variable Calculus: Early Transcendentals | 8th Edition

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Problem 90

Let an S1 1 1 n D n . (a) Show that if 0 < a , b, then bn11 2 an11 b 2 a , sn 1 1dbn (b) Deduce that bn fsn 1 1da 2 nbg , an11 . (c) Use a 1 1 1ysn 1 1d and b 1 1 1yn in part (b) to show that han j is increasing. (d) Use a 1 and b 1 1 1ys2nd in part (b) to show that a2n , 4. (e) Use parts (c) and (d) to show that an , 4 for all n. (f) Use Theorem 12 to show that limn l  s1 1 1ynd n exists. (The limit is e. See Equation 3.6.6.)

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##### ISBN: 9781305270336

Single Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336. The full step-by-step solution to problem: 90 from chapter: 11.1 was answered by , our top Calculus solution expert on 03/19/18, 03:29PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 95 chapters, and 5427 solutions. The answer to “Let an S1 1 1 n D n . (a) Show that if 0 < a , b, then bn11 2 an11 b 2 a , sn 1 1dbn (b) Deduce that bn fsn 1 1da 2 nbg , an11 . (c) Use a 1 1 1ysn 1 1d and b 1 1 1yn in part (b) to show that han j is increasing. (d) Use a 1 and b 1 1 1ys2nd in part (b) to show that a2n , 4. (e) Use parts (c) and (d) to show that an , 4 for all n. (f) Use Theorem 12 to show that limn l  s1 1 1ynd n exists. (The limit is e. See Equation 3.6.6.)” is broken down into a number of easy to follow steps, and 119 words. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8. Since the solution to 90 from 11.1 chapter was answered, more than 210 students have viewed the full step-by-step answer.

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