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Unformatted text preview: this assignment to answer the following problems: 3. Exercise 1(c) on page 52 of the text. 4. Exercise 2 on page 52 of the text. 5. Exercise 3 on page 52 of the text. 6. Prove the following theorem: If a sequence n s converges to s, then the sequence n s converges to s . In other words, if s s n n = ∞ → lim , then s s n n = ∞ → lim . Hint : What needs to be proved is that for ∈ there is a number N so that when n > N, < ∈-s s n . Since ), )( ( ) ( s s s s s s n n n +-=-it follows that s s s s s s n n n +-=-. That means s s s s s s s s s n n n n-≤ +-=-....
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This note was uploaded on 03/20/2012 for the course MATH 345 taught by Professor Michael during the Spring '12 term at University of Massachusetts Boston.
- Spring '12