Abstract
The idea of convergence of a series is introduced and numerous tests for convergence are devised. The concepts of absolute and conditional convergence are developed and their influence on the permissibility of reordering the terms of a series is explored. After a discussion of products of series, power series are introduced. The exponential, sine and cosine functions are defined as special cases of power series, and their fundamental properties are derived.
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Little, C.H.C., Teo, K.L., van Brunt, B. (2015). Series. In: Real Analysis via Sequences and Series. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2651-0_3
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DOI: https://doi.org/10.1007/978-1-4939-2651-0_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2650-3
Online ISBN: 978-1-4939-2651-0
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