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GoodmanW98T3

# GoodmanW98T3 - (a[10 points ∞ X n =1 n 2 1 n 4 n(b[10...

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Math 21H Mar. 24, 1998 Test #3 Name: Read each question carefully, and be sure to show clearly how you got your answers as well as what your answers are. 1. [10 points] Does the sequence ( - 1) n n 2 1 + n 3 converge? Explain. 2. [10 points] Find the sum of this series: X n =0 3 ( - 1) n 4 n 3. For each of the following, determine whether the series is absolutely convergent, condition- ally convergent, or divergent, and say clearly how you know. (a) [10 points] X n =1 ( - 2) n n 3 n +1 (b) [10 points] X n =1 cos( nπ/ 6) n n (c) [10 points] X n =1 ( - 1) n n ln n 4. Test each series for convergence and say what test you are using:
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Unformatted text preview: (a) [10 points] ∞ X n =1 n 2 + 1 n 4 + n (b) [10 points] ∞ X n =1 3 n 4 n-5 5. [10 points] Write out the ﬁrst three partial sums ( s 1 , s 2 , and s 3 ) of the series ∞ X n =1 2 n n ! . 6. [10 points] Give an example of an inﬁnite series X a n which diverges, even though lim n →∞ a n = 0. 7. [10 points] Suppose a series ∑ a n has positive terms ( a n > 0) and its partial sums satisfy s n < 54 for all n . Explain why the series must be convergent....
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