# Determine whether the geometric series is convergent or divergent

23-32 Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 23. 3 – 4 + 1 – 94 + … 24. 4 + 3 + + 16+ 25. 10 – 2 + 0.4 0.08 + … 26. 2 + 0.5 + 0.125 + 0.03125 + … 5 27. 12(0.73)n-1 28. Σ η=1 n=1 TT” 00 3n+1 (-3)n-1 29. Σ 4″ 30. Σ (-2)” Ma 8 e2: 2η 6.2 2n-1 31. Σ 32. Σ n=1 6″-1 n=1 3″ 33. 1 1 + + + 3 6 9 1 + 12 1 15 + 34. 1 2 3 4 5 6 + + + + + 2 3 4 5 6 7 +… 35. 2 4 + + 5 25 8 + 125 16 + 625 32 3125 36. 1 2 1 + + + 3 9 27 2 81 + 1 2 + 243 729 +… 90 2 +η 37. Σ 1 – 2η 38. Σ k ka k2 – 2k +5 39. Σ 31+14-1 40. [(-0.2)” + (0.6)”-‘] 41. Σ 1 4 +e” 42. Σ 2″ + 4″ e” 1 43. Σ (sin 100)* k=1 44. Σ π=11+ ()” 46. Σ (42) 2 -k 45. Σ 1n n? +1 2n2 +1 η=1 47. Σ arctan n 48. Σ(3) Σ( * ) 30. Σ 49. Σ 50. Σ. 1. Draw a picture to show that 7. Σ η? +1 8. Σ ne-n’ 3 Rn Σ 1 1.5 < JI dr 1 2 η. 9. Σ 10. Σ tan in π= 1 + η? =2 η(Ιn n) What can you conclude about the series? 2. Suppose f is a continuous positive decreasing function for x> 1 and a, = f(n). By drawing a picture, rank the follow- ing three quantities in increasing order: 11-28 Determine whether the series is convergent or divergent. 11. Σε 12. Ση-09999 6 Jf() dr Σ α Σ α, 1 d, 13. 1 + 1 8 + + 1 64 + +… 125 14. 1 1 1 + + + 5 7 9 1 11 + 1 13 + 3-10 Use the Integral Test to determine whether the series is convergent or divergent. 3. Ση-3 4. Ση-03 15. 1 3 1 11 + 1 15 + + 7 + 1 19 +… -! 2 5. Σ 16. 1 + 1 6. Σ 1-1 (3η – 1) 1 1 1 1 + + + 22 33 4/4 55 + 1-1 5η 1 Tests for Convergence/Divergence of Series (CHAPTER 11) 1. nth-Term Test for Divergence (ONLY for Divergence!) 2. Geometric-Series Test (r = ?) 3. p-Series Test (p = ?) 4. Integral Test (Stay Away!) Series (Convergent/Divergent) Write several complete simple sentences about how each series is convergent or divergent, including which test is applied! (Hypothesis (Criteria), Conclusion (Converge/Diverge), & EXACT Test Name!) P748: 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 50 (SECTION 11.2) (Ignore the sum!) P758: 3, 4, 11, 12, 13, 16 (SECTION 11.3) (Ignore Integral Test!)
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