Unformatted text preview: n ). Previous Exam Questions (for Practice) 2. ( 7 points ) Find all x for which the series below converges. Find all x for which the series diverges. When the series converges, determine whether the convergence is absolute or conditional. Show your results in a diagram. ∞ X n =1 (1) n (3 x ) n √ n . 2. ( 40 points ) Determine whether the given series converges absolutely, converges conditionally, or diverges. Explain clearly any comparisons you make, and why any test you use can be applied. (a) ∞ X k =1 (1) k k 2 k (3 k )! . (b) ∞ X k =1 (1) k 5 k k 2 . 4. ( 30 points ) Find the radius of convergence of the given series, and the set of points for which it converges. Find the set of points for which the series diverges. When the series converges, determine whether the convergence is absolute or conditional. (a) ∞ X k =0 (1) k x 2 k 4 k . (b) ∞ X k =0 (1) k (3 x + 1) k √ k ....
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 Summer '05
 Dodson
 Mathematical Series

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