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Published in:
2015 | OriginalPaper | Chapter
2. Sequences
Authors : Charles H. C. Little, Kee L. Teo, Bruce van Brunt
Published in: Real Analysis via Sequences and Series
Publisher: Springer New York
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Abstract
The idea of convergence of a sequence to a limit is introduced and properties of limits are discussed. The sandwich theorem is proved, then used as a tool for evaluating limits. Cauchy’s principle is introduced and used to prove the Bolzano–Weierstrass theorem. The chapter concludes with discussions of monotonic and unbounded sequences.