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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- Spring '11
- Calculus, Mathematical analysis, Limit of a sequence