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HH_Sec_9_4

# HH_Sec_9_4 - Math 10B Lecture Examples Section 9.4 Tests...

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(9/1/08) Math 10B. Lecture Examples. Section 9.4. Tests for convergence Example 1 Does the series summationdisplay n =0 (0 . 6) n n + 1 converge? Answer: summationdisplay n =0 (0 . 6) n n + 1 converges by the Comparison Test with the convergent Geometric Series summationdisplay n =0 (0 . 6) n . (All but the first partial sum of summationdisplay n =0 (0 . 6) n n + 1 in Figure A1a is less than the corresponding partial sum of summationdisplay n =0 (0 . 6) n in Figure A1b.) N 10 20 y 1 2 N 10 20 y 1 2 y = N summationdisplay n =0 (0 . 6) n n + 1 y = N summationdisplay n =0 (0 . 6) n Figure A1a Figure A1b Example 2 Does summationdisplay n =1 10 cos(3 n ) n 3 / 2 converge? Answer: summationdisplay n =1 10 cos(3 n ) n 3 / 2 converges. Example 3 Does summationdisplay n =2 1 n - 1 converge or diverge? Answer: summationdisplay n =1 1 n - 1 diverges. Example 4 Does summationdisplay n =0 2 n + 10 5 n converge or diverge? Answer: summationdisplay n =0 2 n + 10 5 n converges by the Limit Comparison Test with the convergent geometric series summationdisplay n =0 ( 2 5 ) n . Lecture notes to accompany Section 9.4 of Calculus by Hughes-Hallett et al 1

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Math 10B. Lecture Examples. (9/1/08)
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HH_Sec_9_4 - Math 10B Lecture Examples Section 9.4 Tests...

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