11.4 Comparison Tests-solutions

11.4 Comparison Tests-solutions - im(gi768 11.4 Comparison...

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im (gi768) – 11.4 Comparison Tests – sadun – (53088) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Determine whether the series s k = 1 3 k 6 + 6 converges or diverges. 1. series is divergent 2. series is convergent correct Explanation: Note frst that the inequalities 0 < 3 k 6 + 6 < 3 k 6 hold For all n 1. On the other hand, by the p -series test, the series s k = 1 3 k 6 is convergent because p = 6 > 1. By the comparison test, thereFore, the given series is convergent . 002 10.0 points Determine whether the series s n = 1 6 4 + 5 n converges or diverges. 1. series is convergent correct 2. series is divergent Explanation: Note frst that the inequalities 0 < 6 4 + 5 n < 6 5 n hold For all n 1. On the other hand, the series s n = 1 6 5 n converges because it is a geometric series with | r | = 1 5 < 1 . By the comparison test, thereFore, the series is convergent . 003 10.0 points Determine whether the series s k = 1 4 + cos k 3 k converges or diverges. 1. series is convergent correct 2. series is divergent Explanation: We use the Comparison Test with a k = 4 + cos k 3 k , b k = 5 3 k . ±or then 0 < a k b k , since 1 cos k 1. Thus the series s k = 1 4 + cos k 3 k converges iF the series s k = 1 5 3 k converges. But this last series is a geometric series with | r | = 1 3 < 1 ,
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im (gi768) – 11.4 Comparison Tests – sadun – (53088) 2 hence convergent. Consequently, the given series is convergent . 004 10.0 points Which of the following series ( A ) s n = 1 4 n 5 n 2 + 2 ( B ) s n = 1 p 2 3 P n ( C ) s n = 15 p 5 6 P n converge(s)? 1. B only 2. A, B, and C 3. C only 4. A and B only 5. B and C only correct Explanation: ( A ) Because of the way the n th term is deFned as a quotient of polynomials in the series, use of the integral test is suggested.
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  • Fall '07
  • Sadler
  • Calculus, Mathematical Series

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