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Unformatted text preview: 1 2 , not 0. 6. ∞ X n =1 (1) n (1 . 1) n n 4 DIVERGES. In fact, (1 . 1) n n 4 approaches ∞ . Easiest for this problem is probably to use the ratio test. 7. ∞ X n =1 (1) n n √ n 4 + 2 CONDITIONALLY CONVERGES. The “positive part” is less than b n = n √ n 4 = n n 2 = 1 n . We can use the limit comparison test to show that the sum of the absolute values is divergent. 8. ∞ X n =1 (1) n n 2 2 n n ! ABSOLUTELY CONVERGES. Use the ratio test. Note that ( n + 1) 2 2 n +1 ( n + 1)! · n ! n 2 2 n = ( n + 1) 2 n 2 · 1 n + 1 · 2 1 , a product of three “chunks” that approach 1, 0, and 2 respectively. 2...
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 Spring '08
 wang
 Math, Mathematical Series

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