hw4 - n 2(101) n . You may assume any statements made in...

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Calculus II, Homework 4 October 9, 2007 Fun with sequences ! 1. Determine whether the integral Z 0 dx x + x 3 is convergent or divergent. Explain. 2. Does the sequence ± (ln n ) 2 n ² converge? If so evaluate the limit. 3. Show that { n 2 + n - n } converges to 1 2 . Hint: multiply by a “conjugate”. 4. Show that { (101 n + 100 n ) 1 /n } converges to 101. Hint: 101 n 101 n + 100
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Unformatted text preview: n 2(101) n . You may assume any statements made in class. 5. Consider the sequence a 1 = 2, a n +1 = 2 + a n . You may assume it converges (extra credit: show that it actually does converge. hint: show it is a bounded monotone sequence). What is lim n a n ? 1...
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