Math.112HW9(2008-9,Spring)

Math.112HW9(2008-9,Spring) - conditionally convergent...

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“Due on April 20, up to 12:50 p.m. ” Math112 Homework 9 Question 1. Let g be a decreasing differentiable function on (100 , ) . Assume that lim x →∞ x 3 g 0 ( x ) = 0 and lim x →∞ g ( x ) = 1 . Show that the series X ( 1 - g ( n ) ) is convergent. Question 2. For which values of p is the series X ( - 1) n sin ± 1 n p ² absolutely convergent,
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Unformatted text preview: conditionally convergent, divergent? Question 3. Is the series X (-1) n ( n √ 2-1) conditionally convergent? Question 4. For which values of q is the series X (-1) n 1 n ln q n absolutely convergent, conditionally convergent, divergent? 1...
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