Sequences and Series

Abbott, Stephen

doi:10.1007/978-1-4939-2712-8_2

Sequences and Series

Stephen Abbott⁴

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Part of the book series: Undergraduate Texts in Mathematics ((UTM))

Abstract

Consider the infinite series

$$\displaystyle{\sum _{n=1}^{\infty }\frac{(-1)^{n+1}} {n} = 1 -\frac{1} {2} + \frac{1} {3} -\frac{1} {4} + \frac{1} {5} -\frac{1} {6} + \frac{1} {7} -\frac{1} {8} + \cdots \,.}$$

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Notes

1.
A thorough account of the logical dependence between these various results can be found in [23].

Bibliography

James Propp, “Real Analysis in Reverse,” American Mathematical Monthly, Volume 120, May 2013, pp. 392–408.
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Authors and Affiliations

Department of Mathematics, Middlebury College, Middlebury, VT, USA
Stephen Abbott

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Stephen Abbott
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Abbott, S. (2015). Sequences and Series. In: Understanding Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2712-8_2

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DOI: https://doi.org/10.1007/978-1-4939-2712-8_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2711-1
Online ISBN: 978-1-4939-2712-8
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