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Homework #6 Sequences Read section 2.2 Exercises from the text: Pages 72-74: #2a,g,h, #5, #6, #12, #21 Here are some other exercises in thought and logic that you will most certainly find interesting. 1. Let A be a bounded subset of with sup( A) S , Show that there exists a sequence an with an A for each n , such that an converges to S. 2. If an converges to a, and bk a1 a2 a3 ak , show that bn also converges k to a. In exercise 3-6 determine whether the given statement is true or false: If true prove, if false give a counter-example. 3. If an ≤ cn ≤ bn for all n and Lim an Lim bn L, then Lim cn exists and is equal n n n to L. 4. If {an} and {bn} diverge, then {an + bn} diverges. 5. If an bn for all n , and {an } and {bn } converge to A and B respectively, then A < B. 3 6. The sequence an 5 n converges.