HWK11 - Valenica, Daniel Homework 11 Due: Nov 13 2007, 3:00...

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Unformatted text preview: Valenica, Daniel Homework 11 Due: Nov 13 2007, 3:00 am Inst: Cheng 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points If the n th partial sum of an infinite series is S n = 3 n 2- 2 2 n 2 + 3 , what is the sum of the series? 1. sum = 3 2 correct 2. sum = 11 8 3. sum = 7 4 4. sum = 13 8 5. sum = 5 4 Explanation: By definition sum = lim n S n = lim n 3 n 2- 2 2 n 2 + 3 . Thus sum = 3 2 . keywords: partial sum, definition of series 002 (part 1 of 1) 10 points If the n th partial sum of n =1 a n is given by S n = 4 n + 5 n + 4 , what is a n when n 2? 1. a n = 21 ( n + 4)( n + 5) 2. a n = 21 ( n + 4)( n + 3) 3. a n = 11 ( n + 4)( n + 3) correct 4. a n = 21 n ( n + 4) 5. a n = 11 n ( n + 4) 6. a n = 11 ( n + 4)( n + 5) Explanation: By definition S n = n X k 1 a n = a 1 + a 2 + ... + a n . Thus, for n 2, a n = S n- S n- 1 = 4 n + 5 n + 4- 4( n- 1) + 5 ( n- 1) + 4 . Consequently, a n = 11 ( n + 4)( n + 3) . keywords: partial sum, definition of series 003 (part 1 of 1) 10 points Determine whether the series 3- 9 2 + 27 4- 81 8 + is convergent or divergent, and if convergent, find its sum. 1. convergent with sum = 2 2. convergent with sum = 3 3. convergent with sum = 4 5 4. series is divergent correct Valenica, Daniel Homework 11 Due: Nov 13 2007, 3:00 am Inst: Cheng 2 5. convergent with sum = 3 5 Explanation: The infinite series 3- 9 2 + 27 4- 81 8 + = X n = 1 ar n- 1 is an infinite geometric series with a = 3 , r =- 3 2 . But an infinite geometric series n = 1 ar n- 1 (i) converges when | r | < 1 and has sum = a 1- r while it (ii) diverges when | r | 1 . Consequently, the given series is divergent . keywords: infinite series, geometric series, di- vergent 004 (part 1 of 1) 10 points Determine whether the series X n = 1 4 n 5 n + 3 is convergent or divergent, and if convergent, find its sum. 1. divergent correct 2. convergent with sum = 5 4 3. convergent with sum = 4 5 4. convergent with sum = 1 2 5. convergent with sum = 2 Explanation: The infinite series X n =1 a n is divergent when lim n a n exists but lim n a n 6 = 0 . Note for the given series, a n = 4 n 5 n + 3 = 4 5 + 3 n , so lim n a n = lim n 4 n 5 n + 3 = 4 5 6 = 0 . Thus the given series is divergent . keywords: 005 (part 1 of 1) 10 points Determine whether the series X n = 0 2 1 5 n is convergent or divergent, and if convergent, find its sum. 1. divergent 2. convergent, sum = 11 4 3. convergent, sum =- 11 4 4. convergent, sum = 5 3 5. convergent, sum = 5 2 correct Valenica, Daniel Homework 11 Due: Nov 13 2007, 3:00 am Inst: Cheng 3 Explanation: The given series is an infinite geometric series X n = 0 ar n with a = 2 and r = 1 5 . But the sum of such a series is (i) convergent with sum a 1...
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This homework help was uploaded on 04/16/2008 for the course CALC 303L taught by Professor Cheng during the Fall '07 term at University of Texas at Austin.

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HWK11 - Valenica, Daniel Homework 11 Due: Nov 13 2007, 3:00...

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