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2a.408DF11assign2

# 2a.408DF11assign2 - proportional to the height from which...

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M408D Fall 2011 Assignment 2 Due Friday, September 9 Be sure that you have read and understood sections 12.1 and 12.2 and worked the assigned text exercises before you complete this assignment. You must show suﬃcient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. Homework is to be turned in at the beginning of class. 1. Is the sequence { ln( n + 1) - ln( n ) } monotone? Is it bounded? Find the limit of the sequence or show that it doesn’t exist. 2. Suppose that when a ball is dropped to the ﬂoor, it rebounds to a height
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Unformatted text preview: proportional to the height from which it is dropped. A ball is dropped from a height of 6 feet and travels a total distance of 21 feet before it stops bouncing. Find the height to which the ball rebounds initially. 3. Determine whether or not the series ∞ X n =0 1 n 2 + 4 n + 3 converges. If it converges, ﬁnd the sum. 4. Suppose that ∞ X n =1 a n is a series and that a n 6 = 0 for all n ≥ 1. (a) Suppose that ∞ X n =1 a n converges. Explain clearly why ∞ X n =1 1 a n must diverge. (b) Now suppose that ∞ X n =1 a n diverges. Show by giving examples that ∞ X n =1 1 a n may converge or may diverge. 1...
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