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Unformatted text preview: terms, prove that s-s 6 ≤ 1 729 . 4. Determine whether or not the following series are convergent. (a) ∞ X n =2 (-1) n ln n (b) ∞ X n =1 (-1) n ( √ n 2 + 2 n-n ) (c) ∞ X n =1 (-1) n +1 e 1 /n n 5. Explain why each series below converges. Then find the smallest integer n such that the n th partial sum s n will approximate the actual sum of the series s with error less than the given bound. (a) ∞ X n =1 n (-1) n-1 n 2 + 1 , with error less than 10-3 (b) ∞ X n =1 (-1) n +1 n 2 2 n , with error less than 10-3 . (c) ∞ X n =1 (-1) n ( n !) 2 , with error less than 10-6 . 6. Does the series ∞ X n =0 = √ 2 sin ± (2 n + 1) π 4 ² cos ³ nπ 2 ´ (-1) n ( n + 1)-1 converge or diverge. Justify your answer. 2...
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- Fall '07
- Anoymous
- Math, Calculus, n=1
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