# hw7 - 4 Determine whether the series is convergent or...

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MATH 138: Calculus 2 Assignment #7 (Corrected) Due: 12:30 p.m., Friday, November 12 Fall 2010 1. Show that the sequence deﬁned by a 1 = 3 , a n +1 = 1 4 - a n for n 1 satisﬁes 0 < a n 3 and is decreasing. Deduce that the sequence is convergent and ﬁnd its limit. 2. Determine whether the series is convergent or divergent. If it is convergent, ﬁnd the sum. If it is divergent, explain why. (a) X n =1 12 ( - 5) n (b) X n =1 2 n 2 - 1 n 2 + 1 (c) X n =1 1 n ( n + 2) (d) X n =1 1 + 2 n 3 n 3. Express the number 0 . 73 = 0 . 73737373 ... as a ratio of integers.
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Unformatted text preview: 4. Determine whether the series is convergent or divergent (a) ∞ X n =1 1 2 n (b) ∞ X n =1 n + 1 2 n-3 (c) ∞ X n =1 n 2 n 4 + 1 (d) ∞ X n =1 √ n + 1 n (e) ∞ X n =1 n 2 + 5 n n 3 + n + 1 (f) ∞ X n =1 √ n n 2 + 1 The following problems are only recommended, not for submission. • Stewart: Section 11.1 Exercises 69, 70, 79; Section 11.2 Exercises 27, 33, 23, 41, 43, 47, 49; Section 11.4 Exercises 3, 5, 21, 15....
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