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In Exercises 1-4, use the comparison test to confirm the statement. 1. 2 diverges, so diverges. n-3 2. 2 converges, so n+2 converges. 3. converges, so converges. converges, so 2 (n Σ 4. converges. 7n+1 IM IM IM: IM M17 IM: IM: IM

In Exercises 1-4, use the comparison test to confirm the statement. 1. 2 diverges, so diverges. n-3 2. 2 converges, so n+2 converges. 3. converges, so converges. converges, so 2 (n Σ 4. converges. 7n+1 IM IM IM: IM M17 IM: IM: IM

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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ngie Vari... Page 525 of 745 Q Search Exercises and Problems for Section 9.4 Online Resource: Additional Problems for Section 9.4 EXERCISES In Exercises 1-4, use the comparison test to confirm the In Exercises 15-21, use the ratio test to decide whether the series converges or diverges. statement, 00 . Σ- άνerges, 2a diverges. so 00 15. Σ 00 n-3 16. E 1 (2n)! 2 00 2. 25 converges, so Σ 00 n² +2 converges. 17. E (n!)? (2n)! 18. ne 1 3. converges, so Σ e converges. 19. S n!(n+ 1)! (2n)! 00 20. n! 00 EG) converges, so 4. 3n Σ 21. 2 7n+1) converges. n'+1 In Exercises 5-8, use end behavior to compare the series to a p-series and predict whether the series converges or diverges. In Exercises 22-32, use the limit comparison test to deter- mine whether the series converges or diverges. 00 5n + 1 by comparing to 00 22. 5. Sn' +1 n* + 2n + 2n 00 3n2 n+4 6. E n3 + 5n – 3 00 23. E() 1+n 3n by comparing to GY 00 n-4 nt + 3n? +7 8. (Hint: lim,(1+1/n)" = e.] Vn + n? +8 00 24. (1- cos - ). by comparing to In Exercises 9-14, use the.comparison test to determine whether the series converges. 00 25. 2 n -7 26. Sn+1 n +2 9. 5 10. E 1 00 n +1 3" +1 n -2n +n+1 27. 28. n - 2 3" – 1 00 12, 51 Inn 2 11. 30. ( ) 1 29. E |2Vn+ Vn+2 n* + e" 2n-1 2n 14. 5 2" + 1 n2" - 1 00 n sin' n n +1 13. 4 sin n+n 31. 32. cos n + e" n ten 7See Walter Rudin, Principles of Mathematical Analysis, 3rd ed. (New York: McGraw-Hill, 1976), pp. 76-77, MAR étv 30 MacBook Pro 14 #3 2$ % & @ 8. 4 W EIR IM: IM³ CO
Transcribed Image Text:ngie Vari... Page 525 of 745 Q Search Exercises and Problems for Section 9.4 Online Resource: Additional Problems for Section 9.4 EXERCISES In Exercises 1-4, use the comparison test to confirm the In Exercises 15-21, use the ratio test to decide whether the series converges or diverges. statement, 00 . Σ- άνerges, 2a diverges. so 00 15. Σ 00 n-3 16. E 1 (2n)! 2 00 2. 25 converges, so Σ 00 n² +2 converges. 17. E (n!)? (2n)! 18. ne 1 3. converges, so Σ e converges. 19. S n!(n+ 1)! (2n)! 00 20. n! 00 EG) converges, so 4. 3n Σ 21. 2 7n+1) converges. n'+1 In Exercises 5-8, use end behavior to compare the series to a p-series and predict whether the series converges or diverges. In Exercises 22-32, use the limit comparison test to deter- mine whether the series converges or diverges. 00 5n + 1 by comparing to 00 22. 5. Sn' +1 n* + 2n + 2n 00 3n2 n+4 6. E n3 + 5n – 3 00 23. E() 1+n 3n by comparing to GY 00 n-4 nt + 3n? +7 8. (Hint: lim,(1+1/n)" = e.] Vn + n? +8 00 24. (1- cos - ). by comparing to In Exercises 9-14, use the.comparison test to determine whether the series converges. 00 25. 2 n -7 26. Sn+1 n +2 9. 5 10. E 1 00 n +1 3" +1 n -2n +n+1 27. 28. n - 2 3" – 1 00 12, 51 Inn 2 11. 30. ( ) 1 29. E |2Vn+ Vn+2 n* + e" 2n-1 2n 14. 5 2" + 1 n2" - 1 00 n sin' n n +1 13. 4 sin n+n 31. 32. cos n + e" n ten 7See Walter Rudin, Principles of Mathematical Analysis, 3rd ed. (New York: McGraw-Hill, 1976), pp. 76-77, MAR étv 30 MacBook Pro 14 #3 2$ % & @ 8. 4 W EIR IM: IM³ CO
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