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Problems
In Problems 1-13 find the nth partial sum, determine whether the series converges, and find the sum when it exists. 6 (a1 - a2) + (a2 - a3) + ... + (an - an+ l) + ... where limn→∞ an = 0. This is called a telescoping series. In Problems 14-19, show that the series diverges. 19 ln 1 + ln 2 + ln 3 + ...+ ln n + ... 20 A ball bounces along a street. On each bounce it goes f as far as it did on the previous bounce. If the first bounce is one foot long, how far will the ball go before it stops bouncing? 21 Two students are sharing a loaf of bread. Student A eats half of the loaf, then student B eats half of what's left, then A eats half of what's left, and so on. How much of the loaf will each student eat? 22 In the Problem 21, how much will each student eat if only 1/5 of the remaining loaf is eaten at each turn? 23 Three students A, B, C take turns eating a loaf of bread, taking ⅓ of the remaining loaf at each turn. How much will each student eat?
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