M408L_HW12 - hyun (hh7953) HW12 gogolev (57440) 1 This...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: hyun (hh7953) HW12 gogolev (57440) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 10.0 points If the n th partial sum of n =1 a n is given by S n = 3 n + 5 n + 4 , what is a n when n 2? 1. a n = 7 ( n + 4)( n + 3) correct 2. a n = 7 n ( n + 4) 3. a n = 17 ( n + 4)( n + 5) 4. a n = 17 ( n + 4)( n + 3) 5. a n = 7 ( n + 4)( n + 5) 6. a n = 17 n ( n + 4) Explanation: By definition S n = n summationdisplay k 1 a n = a 1 + a 2 + . . . + a n . Thus, for n 2, a n = S n S n 1 = 3 n + 5 n + 4 3( n 1) + 5 ( n 1) + 4 . Consequently, a n = 7 ( n + 4)( n + 3) . 002 10.0 points Determine whether the series summationdisplay n = 0 2 (cos n ) parenleftbigg 3 4 parenrightbigg n is convergent or divergent, and if convergent, find its sum. 1. convergent with sum 8 2. convergent with sum 8 7 3. divergent 4. convergent with sum 8 7 correct 5. convergent with sum 8 6. convergent with sum 7 8 Explanation: Since cos n = ( 1) n , the given series can be rewritten as an infinite geometric series summationdisplay n =0 2 parenleftbigg 3 4 parenrightbigg n = summationdisplay n = 0 a r n in which a = 2 , r = 3 4 . But the series n =0 ar n is (i) convergent with sum a 1 r when | r | < 1, and (ii) divergent when | r | 1. Consequently, the given series is convergent with sum 8 7 . 003 10.0 points hyun (hh7953) HW12 gogolev (57440) 2 Determine whether the series summationdisplay n = 1 n 2 3 n 2 + 5 is convergent or divergent, and if convergent, find its sum. 1. divergent correct 2. convergent with sum = 3 3. convergent with sum = 8 4. convergent with sum = 1 8 5. convergent with sum = 1 3 Explanation: The infinite series summationdisplay n =1 a n is divergent when lim n a n exists but lim n a n negationslash = 0 . Note for the given series, a n = n 2 3 n 2 + 5 = 1 3 + 5 n 2 , so lim n a n = lim n n 2 3 n 2 + 5 = 1 3 negationslash = 0 . Thus the given series is divergent . 004 10.0 points Determine whether the infinite series summationdisplay n = 1 3 n 2 n 5 n converges or diverges, and if it converges, find its sum. 1. converges with sum = 2 3 2. converges with sum = 5 6 correct 3. series diverges 4. converges with sum = 1 2 5. converges with sum = 1 4 6. converges with sum = 1 Explanation: An infinite geometric series n =1 a r n 1 (i) converges when | r | < 1 and has sum = a 1 r , while it (ii) diverges when | r | 1 . Now summationdisplay n = 1 3 n 5 n = summationdisplay n = 1 3 5 parenleftbigg 3 5 parenrightbigg n 1 is a geometric series with a = r = 3 5 < 1....
View Full Document

Page1 / 13

M408L_HW12 - hyun (hh7953) HW12 gogolev (57440) 1 This...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online