Exercises2 - 1 1 1 1 n n n ∞ = ∑ for absolute...

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Exercises - 2 1- Find the radius of convergence R and the interval of convergence I of the power series 0 ( 1) ( 1) 2 ( 1) k k k k k x k = - + + . (do not forget to check the end points ) 2- Find the sum of the convergent series 1 ( 1) n n n e n = - 3- Determine whether the following series converges or diverges: a) 2 120 n n n = - b) 2 120 1 cos n n n n = + c) 10 1 10 n n n = d) 1 3 1 n n n n = + e) 1 (ln ) n n n n = f) 1 2 n n n = - 4- Check the series
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Unformatted text preview: 1 1 ( 1) 1 n n n ∞ =-+ ∑ for absolute convergence. Is it conditionally convergent? 5-The series 3 5 7 9 11 sin 3! 5! 7! 9! 11! x x x x x x x = -+-+-+ m converges to sinx for all x. Find the series for cos x, a) using term by term differentiation and b) using term by term integration For what values of x should the series converge?...
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This note was uploaded on 05/09/2010 for the course MATHEMATIC 120 taught by Professor A during the Spring '10 term at Middle East Technical University.

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