Series Review - Math 2224 Sequence/Series Review I. Write...

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Math 2224 – Sequence/Series Review I . Write the first four terms of each sequence. Determine whether each one converges or diverges. If it converges, find the limit. 1. a n = 1 5 n 4 n 4 + 8 n 3 2. a n = sin n n 3. a n = 2 ( ) n n 2 II . Determine the convergence or divergence of each of the following series. State which test you are using. Find the sum for any convergent geometric or telescoping series. 1. 1 ( ) n + 1 n = 1 n n + 1 2. n 2 5 n 2 + n + 9 n = 0 3. ( ) n = 1 1 n 4. 2 n 1 2 n n = 1 5. π n 1 e n n = 1 6. 1 ( ) n + 1 ln n n = 2 7. + 1 n n = 1 8. sin 1 n n = 1 sin 1 n + 1 9. 1 + 1 n n n = 1 10. 1 ( ) n = 2 n + 1 ln n ln n 2 11. arctan n n = 1 12. 1 n 2 n ( ) n = 1 13. 2 n n + 2 ( ) n = 1 14. e n n 3 n = 1 15. 3 n n + 3 ( ) ! 3! n ! n = 1 16. ln n n n = 3 III . The following alternating series converges. 1 ( ) n + 1 n = 1 1 5 . 1. Estimate the magnitude of the error involved in using the sum of the first 6 terms to approximate the sum of the entire series.
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Series Review - Math 2224 Sequence/Series Review I. Write...

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