# hw0902 - Homework problems week of Sept 2 Practice problems...

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Homework problems, week of Sept. 2 Practice problems These problems will not be collected or graded. They are intended to help you understand the main ideas. (They’re also examples of midterm problems.) 1. Prove the generalized triangle inequality: if { x n } N n = 1 is any finite sequence of real numbers, then N n = 1 x n N n = 1 | x n | . 2. Evaluate the following limits: (a) lim n n 2 + 2 n - 1 n 2 - 3 n + 2 (b) lim n n + n - 1 2 n 2 - 3 n 3. Construct an infinite bounded sequence, each of whose elements is distinct, that has exactly three accumulation points. Homework problems Please write up these problems and turn them in at the beginning of class on Tuesday, Sept. 9. The usual collaboration policies apply (see the course syllabus). Definition. Let S be a subset of the real numbers. The supremum of S , denoted sup S , is the least upper bound of S (whenever it exists). The infimum of S , denoted inf S , is the greatest lower bound of S (whenever it exists).

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