# A07 - error in using s 10 as an approximation to the full...

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Math 138 – Fall 2011 Assignment 7 Due Monday Nov 7 (in the drop box by 12 noon) Hand in the following: 1. Determine whether or not the following series are convergent. If so, ﬁnd the sum . If not, explain why. (a) X n =1 1 + 2 n 4 n - 1 (b) X n =1 1 n ( n + 2) (c) X n =1 e 1 /n (d) X n =2 1 n 3 - n (This one is tricky. You may want to come back to it) 2. Find the value of c if X n =2 (1 + c ) - n = 2. 3. (a) Explain why the integral test can be used to determine the con- vergence of the series X n =1 n n 4 + 1 . Then show that the series is convergent. (b) Calculate the partial sum s 10 , and give an upper bound on the

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Unformatted text preview: error in using s 10 as an approximation to the full sum of the series. 4. (a) Explain why the integral test can be used to determine the con-vergence of the series ∞ X n =2 1 n (ln n ) 2 . Then show that the series is convergent. (b) Find n such that the n th partial sum of the series, s n , estimates the actual sum with error at most 1 100 . 5. Determine whether the following series converge or diverge. (a) ∞ X n =0 ne-n 2 (b) ∞ X n =3 1 n ln n √ ln ln n (c) ∞ X n =0 n 2 1 + n √ n 2...
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A07 - error in using s 10 as an approximation to the full...

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