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### seriespractice2key

Course: WORKSHEETS 141, Fall 2009
School: Penn State
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series The in the following problems converge: 3,4,5,6,8,10,14,16,19,20,21,22,26,29,31,33,34,35,36,38,39,40,41,42,45,46,52,58,59,60 series The in the other problems diverge. 1

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Penn State - WORKSHEETS - 141
SAMPLE PROBLEMS Determine whether each of the following series converges or diverges. 1. 4. 7. 10. 13. 16. 19. 22. 25. 28. 31. 34. 37. 40. 43. 46. 49. 52. 55. 58.1 n2. 5. 8. 11. 14. 17. 20. 23. 26.2 n n1 n sin2 n n2 cos n+5 n2 ln n n 1 n2 ln n 1 n(ln
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Series + Series + Series + . . . by Linda Schobert Determine whether each series is absolutely convergent, conditionally convergent, or divergent. n (n + 1)2 2n 1 n 1) tan 3) 2) 2 2n2 + 1 n! n=1 n=1 n=1 (1)n (1 n) 4) 2n n=1 cos n 5) n n+1 n=1 8n+2 8) nn
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Relative Rates of GrowthMany of the common functions tend to take bigger and bigger values when the argument is getting bigger. In other words, for many common functions f (x) we have lim f (x) = +. Sometimes this limitx+condition is all we need. But o
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Math 141 Power Series Review1) Find the radius and interval of convergence of each power series. (-1)n xn n2 +3 3n xn n! nn (x-3)n (n-1)2n (3x-2)n n3/2 4n+1a)n=0b)n=0 c)n=1 n=0d)n=22) Suppose thatn=0 cn 3n converges andcn 5n diverges. What c
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Math 141 Integration PracticeFor each of the following integrals, decide what method to use. (You could use integration by parts, substitution, a trig identity, or another algebraic method). After you've made your educated guesses, go back and try them o
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Penn State - WORKSHEETS - 141
The series in the following problems converge absolutely: 3,5,6,9,11,13,14 The series in the following problems converge conditionally: 1,7,8,10 The series in the other problems diverge.1
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SAMPLE PROBLEMS Determine whether each of the following series converges absolutely, converges conditionally, or diverges. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.(-1)n n(-1)n n(-1)n n2 (-1)2n+1 n (-1)2n+1 n+3n-4 (-1)n+1 n+3n-4 (-1)n n ln n (
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