# Answer 11.4-11.7 - 1) 6 ( 1 10 5 ) = 0.00001 48. |error|...

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Answer Keys for Even Numbers \$ 11.4 4. converges by the Direct Comparison Test; 1+cos n n 2 2 n 2 and the p-series 1 n 2 converges. 12. converges by the Limit Comparison Test (part 2) when compared with 1 n 2 n=1 , a convergent p-series 0. 16. diverges by the Limit Comparison Test (part 3) with 1 n , the nth term of the divergent harmonic series . 22. converges by the Direct Comparison Test: , the sum of the nth terms of a convergent geometric series and a convergent p-series. \$ 11.5 4. diverges by the Ratio Test: lim n →∞ a n+1 a n = 12. converges by the nth-Root Test: lim n →∞ a n n = 0 < 1 16. converges by the Ratio Test: lim n →∞ a n+1 a n = 1 2 < 1 \$ 11.6 12. converges absolutely by the Direct Comparison Test since which is the nth term of a convergent geometric series. 18. converges absolutely because the series sin n n 2 n=1 converges by the Direct Comparison Test since sin n n 2 1 n 2 46. |error| < (

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Unformatted text preview: 1) 6 ( 1 10 5 ) = 0.00001 48. |error| < |( 1) 4 t 4 | = t 4 < 1 \$ 11.7 4. lim n u n+1 u n < 1 => 1/3<x<1; when x=1/3 we have ( 1) ? n n=1 which is the alternating harmonic series and is conditionally convergent; when x=1 we have 1 n n=1 , the divergent harmonic series (a) the radius is 1/3; the interval of convergence is 1/3 =< x <1 (b) the interval of absolute convergence is 1/3< x <1 (c) the series converges conditionally at x=1/3 12. . lim n u n+1 u n < 1 => 3|x| lim n 1 n+1 < 1 for all x (a) the radius is ; the series converges for all x (b) the series converges absolutely for all x (c) there are no values for which the series converges conditionally 42. (a) thus the derivative of e x is e x itself (b) , which is the general antiderivative of e x (c) ; e x e x =1+0+0+0+0+0+...
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## This note was uploaded on 05/27/2011 for the course ECON 201 taught by Professor Caltech during the Spring '10 term at Wisc Eau Claire.

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Answer 11.4-11.7 - 1) 6 ( 1 10 5 ) = 0.00001 48. |error|...

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