Abstract
An infinite series is an expression of the form a 1 + a 2 + a 3 + ⋯, where each a i is a real number. We discuss the question of when an infinite series has a “sum” in a precise sense that we will explain. A series that does have such a sum is said to “converge.” The basic properties of convergence of infinite series are rigorously proven. In particular, it is shown that every “infinite decimal” converges.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Rosenthal, D., Rosenthal, D., Rosenthal, P. (2018). An Introduction to Infinite Series. In: A Readable Introduction to Real Mathematics. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-00632-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-00632-7_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00631-0
Online ISBN: 978-3-030-00632-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)