SalasSV_11_07_ex - 686 CHAPTER 11 INFINITE SERIES and apply...

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EXERCISES 11.7 1. Suppose that the power series k = 0 a k x k converges at x = 3, that is, suppose that k = 0 a k 3 k converges. What can you say about the convergence or divergence of the following? (a) k = 0 a k 2 k . (b) k = 0 a k ( 2) k . (c) k = 0 a k ( 3) k . (d) k = 0 a k 4 k . 2. Suppose that the power series k = 0 a k x k converges at x = 3 and diverges at x = 5. What can you say about the convergence or divergence of the following? (a) k = 0 a k 2 k . (b) k = 0 a k ( 6) k . (c) k = 0 a k 4 k . (d) k = 0 ( 1) k a k 3 k . Find the interval of convergence. 3. kx k . 4. 1 k x k . 5. 1 (2 k ) ! x k . 6. 2 k k 2 x k . 7. ( k ) 2 k x 2 k . 8. ( 1) k k x k . 9. 1 k 2 k x k . 10. 1 k 2 2 k x k .
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11.7 POWER SERIES ± 687 11. ± k 100 ² k x k . 12. k 2 1 + k 2 x k . 13. 2 k k x k . 14. 1 ln k x k . 15. k 1 k x k . 16. ka k x k . 17. k 10 k x k . 18. 3
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SalasSV_11_07_ex - 686 CHAPTER 11 INFINITE SERIES and apply...

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