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b. 6. Use the limit comparison test to determine the convergence of the series. 2 11=13"-5 a. b. a. b. C. d. 1 n=1 4√n-1 7. For each of the series below, use at least two of the tests to determine the convergence of the series. Each test should be used at least once. Choose from: nth-term test, p-series test, integral test, limit comparison test, geometric series test, telescoping series test, direct comparison test. Clearly indicate which tests you are using. n=1 a. IM8 IMS IM8 IMS b. e. ¹⁰⁰ tan f. 0⁰ Zn=1 g. Σn=1 n=1 n * (n² + 1)² n-1 2n=1n²√√n n+4" n+6n 1 n=1 n 1 3" +2 00 '2n +3 n=0( 00 n n=1 0⁰0 C. 2n=1 ITAP n (-1)"n² 2 n² +1 COSNT d. Σ(-1)"e-n² e. (-1)+1√√n √√n C. 8. Determine the convergence or divergence of the series. If the series converges, does it converge absolutely or conditionally? E(-1)"+arctann 1 n=n(n² +1) h. Σs (-)" n=0 1 3n²-2n-15 i. n=4 1. Σ n=1 k. 1. Σk=1 1 n+1 n+2 3 n=1 n(n+3) 00 m. Ln=1 00 n. Zn=1 i. k. I. (2k-1)(k²-1) (k+1)(k²+4) e1/n n+1 j. (-1)"+¹¹ √n n=1 n+2 • (−1)”+¹ ln(n+1) S n=1 n sin n=2 n=0 (-1)" Inn COSNT n+1 m. En=1(−1)n-1e2/n

b. 6. Use the limit comparison test to determine the convergence of the series. 2 11=13"-5 a. b. a. b. C. d. 1 n=1 4√n-1 7. For each of the series below, use at least two of the tests to determine the convergence of the series. Each test should be used at least once. Choose from: nth-term test, p-series test, integral test, limit comparison test, geometric series test, telescoping series test, direct comparison test. Clearly indicate which tests you are using. n=1 a. IM8 IMS IM8 IMS b. e. ¹⁰⁰ tan f. 0⁰ Zn=1 g. Σn=1 n=1 n * (n² + 1)² n-1 2n=1n²√√n n+4" n+6n 1 n=1 n 1 3" +2 00 '2n +3 n=0( 00 n n=1 0⁰0 C. 2n=1 ITAP n (-1)"n² 2 n² +1 COSNT d. Σ(-1)"e-n² e. (-1)+1√√n √√n C. 8. Determine the convergence or divergence of the series. If the series converges, does it converge absolutely or conditionally? E(-1)"+arctann 1 n=n(n² +1) h. Σs (-)" n=0 1 3n²-2n-15 i. n=4 1. Σ n=1 k. 1. Σk=1 1 n+1 n+2 3 n=1 n(n+3) 00 m. Ln=1 00 n. Zn=1 i. k. I. (2k-1)(k²-1) (k+1)(k²+4) e1/n n+1 j. (-1)"+¹¹ √n n=1 n+2 • (−1)”+¹ ln(n+1) S n=1 n sin n=2 n=0 (-1)" Inn COSNT n+1 m. En=1(−1)n-1e2/n

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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I need help with Number 6 a to c. 

b. a. 6. Use the limit comparison test to determine the convergence of the series. 2 ¹3"-5 b. a. b. C. d. n=1 00 a. b. 74√/1²-² n=1 ∞0 7. For each of the series below, use at least two of the tests to determine the convergence of the series. Each test should be used at least once. Choose from: nth-term test, p-series test, integral test, limit comparison test, geometric series test, telescoping series test, direct comparison test. Clearly indicate which tests you are using. Σ(-3) n=0 n=1 L√n n 18 IMS IM8 n=1 00 tan e. Σ=1 f. Σn=1 g. Σ=1 n=1 1 ¹3" +2 n=1 n² + ∞ n '2n + 3 00 Ic n=1 n ∞ c. Σ=1 n=0 n ² + 1)² n-1 n² √√n n+4n n=1 n+6n 1 1+= n n COSNT d. Σ(-1)"e-n² (−1)n+1 √n Vn C. \n+ e. Σ(-1)"+¹ arctan n f. Σ=1(-1)" sin 1 n=n(n² +1) h. i. j. k. 8. Determine the convergence or divergence of the series. If the series converges, does it converge absolutely or conditionally? (−1)″ n² n² +1 00 i. j. n=4 Σ n=1\n+1 00 n=1 I. I.E=1 m. 2n=1 Σ= 1 3n²-2n-15 100 n. Σn=₁ sin WW 1 n=1 3 n(n+3) n=0 (2k-1)(k²-1) (k+1)(k²+4) e1/n n (−1)n+¹ n=1 k. † (-1)" In n n=2 1 n+2 1 n n+¹ In(n+1) · COSNT n+1 n+1 (−1)¹+¹ √√n n+2 m. Σã=₁(−1)n-¹e²/n n. Σ=1 (-1)^nn n!
Transcribed Image Text:b. a. 6. Use the limit comparison test to determine the convergence of the series. 2 ¹3"-5 b. a. b. C. d. n=1 00 a. b. 74√/1²-² n=1 ∞0 7. For each of the series below, use at least two of the tests to determine the convergence of the series. Each test should be used at least once. Choose from: nth-term test, p-series test, integral test, limit comparison test, geometric series test, telescoping series test, direct comparison test. Clearly indicate which tests you are using. Σ(-3) n=0 n=1 L√n n 18 IMS IM8 n=1 00 tan e. Σ=1 f. Σn=1 g. Σ=1 n=1 1 ¹3" +2 n=1 n² + ∞ n '2n + 3 00 Ic n=1 n ∞ c. Σ=1 n=0 n ² + 1)² n-1 n² √√n n+4n n=1 n+6n 1 1+= n n COSNT d. Σ(-1)"e-n² (−1)n+1 √n Vn C. \n+ e. Σ(-1)"+¹ arctan n f. Σ=1(-1)" sin 1 n=n(n² +1) h. i. j. k. 8. Determine the convergence or divergence of the series. If the series converges, does it converge absolutely or conditionally? (−1)″ n² n² +1 00 i. j. n=4 Σ n=1\n+1 00 n=1 I. I.E=1 m. 2n=1 Σ= 1 3n²-2n-15 100 n. Σn=₁ sin WW 1 n=1 3 n(n+3) n=0 (2k-1)(k²-1) (k+1)(k²+4) e1/n n (−1)n+¹ n=1 k. † (-1)" In n n=2 1 n+2 1 n n+¹ In(n+1) · COSNT n+1 n+1 (−1)¹+¹ √√n n+2 m. Σã=₁(−1)n-¹e²/n n. Σ=1 (-1)^nn n!
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