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Unformatted text preview: X k =1 1 k 2 + 1 by a partial sum s n . What is the smallest value of n for which s n approximates the sum with error less than 0.001? 3. (a) Explain clearly why it must be true that if X | a k | converges, then X ( a k ) 2 converges. (b) Give examples to show that if X ( a k ) 2 converges, then X a k may con-verge or may diverge. (In other words, the convergence of X ( a k ) 2 gives no information about the convergence of X a k .) 4. Find the smallest integer n so that the n th partial sum s n approximates the sum of the series X k =1 (-1) k +1 k 3 with error less than 0.0001. 1...
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- Spring '11