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42. j=1 ¹3 (²) 243

42. j=1 ¹3 (²) 243

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Answer question 42. Use summation equations. please write out the steps and describe in detail what you are doing during each step.
-1 700 of Determine r and a₁ for each geometric sequence. See Example 3. V 1 29. a3=5, ag = 27. a2=-6, a = -192 28. a₂-8, a7 = 256 625 1 1 100 30. a4= 7₁ ag = 4¹ 31. a3 = 50, a1 = 0.005 32. a3 = 300, a, = 243 128 Use the formula for S, to find the sum of the first five terms of each geometric sequence. In Exercises 37 and 38, round to the nearest hundredth. See Example 5. 33. 2, 8, 32, 128,... 34. 4, 16, 64, 256, ... 9 9 4 4 35. 18,-9, 36. 12, -4, 2² 4 3 9*** 37. a₁ = 8.423, r = 2.859 38. a₁ = -3.772, r = -1.553 Evaluate each sum. See Example 6. 39. (-3)/ 40. Σ(-2)' 41. 48 (¹) 1=1 42. · 243 (²) 43. 24 45. Concept Check Under what conditions does the sum of an infinite geometric series exist? 46. The number 0.999... can be written as the sum of the terms of an infinite geometric sequence: 0.9 + 0.09 +0.009+. Here we have a₁ = 0.9 and r= 0.1. Use the formula for So, to find this sum. Does intuition indicate that this answer is correct? Find r for each infinite geometric sequence. Identify any whose sum diverges. 47. 12, 24, 48, 96,... 48. 2,-10, 50, -250, ... X-S 49. -48, -24, -12, -6, ... 50. 625, 125, 25, 5,... Work each problem. See Examples 7 and 8. S 51. Use lim S, to show that 2+1+ + ++ converges to 4. 818 52. We determined that 1 ++ 1 1 + + 27 converges to using an argument limits. Use the formula for the sum of the terms of an infinito obtain the same result ܐ܂ 44. 9
Transcribed Image Text:-1 700 of Determine r and a₁ for each geometric sequence. See Example 3. V 1 29. a3=5, ag = 27. a2=-6, a = -192 28. a₂-8, a7 = 256 625 1 1 100 30. a4= 7₁ ag = 4¹ 31. a3 = 50, a1 = 0.005 32. a3 = 300, a, = 243 128 Use the formula for S, to find the sum of the first five terms of each geometric sequence. In Exercises 37 and 38, round to the nearest hundredth. See Example 5. 33. 2, 8, 32, 128,... 34. 4, 16, 64, 256, ... 9 9 4 4 35. 18,-9, 36. 12, -4, 2² 4 3 9*** 37. a₁ = 8.423, r = 2.859 38. a₁ = -3.772, r = -1.553 Evaluate each sum. See Example 6. 39. (-3)/ 40. Σ(-2)' 41. 48 (¹) 1=1 42. · 243 (²) 43. 24 45. Concept Check Under what conditions does the sum of an infinite geometric series exist? 46. The number 0.999... can be written as the sum of the terms of an infinite geometric sequence: 0.9 + 0.09 +0.009+. Here we have a₁ = 0.9 and r= 0.1. Use the formula for So, to find this sum. Does intuition indicate that this answer is correct? Find r for each infinite geometric sequence. Identify any whose sum diverges. 47. 12, 24, 48, 96,... 48. 2,-10, 50, -250, ... X-S 49. -48, -24, -12, -6, ... 50. 625, 125, 25, 5,... Work each problem. See Examples 7 and 8. S 51. Use lim S, to show that 2+1+ + ++ converges to 4. 818 52. We determined that 1 ++ 1 1 + + 27 converges to using an argument limits. Use the formula for the sum of the terms of an infinito obtain the same result ܐ܂ 44. 9
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