Chapter 2 - Sequences of Real Numbers

# Chapter 2 - Sequences of Real Numbers - Chapter 2 Sequences...

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Chapter 2 – Sequences of Real Numbers Section 2.1 – The Convergence of Sequences Pg 23, Definition – A sequence of real numbers is a real valued function whose domain is the set of natural numbers. Pg 25, Definition – A sequence is said to converge to the number a provided that for every positive number there is a natural number N such that Pg 25, Proposition 2.1 – The sequence {1/n} converges to 0; that is, Pg 26, Proposition 2.2 – For any number c such that |c| < 1, the sequence converges to 0; that is, Pg 27, Definition – A sequence is said to be bounded provided that there is a number M such that Pg 27, Lemma 2.3 – Every convergent sequence is bounded. Pg 27, Lemma 2.4 – Suppose that the sequence converges to the nonzero number b. Then there is a natural number N such that Pg 28, Theorem 2.5 – Suppose that the sequence converges to the number a and that the sequence converges to the number b. Then the sequence converges, and Also, the sequence converges, and Moreover, if for all n and , then the sequence

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