Abstract
The theory of series of numbers is based on the theory of sequences of numbers. This dependence is the result of both the definition of a series as a sum of all the elements of a sequence and the definition of its convergence as the convergence of a special sequence called the sequence of partial sums. The last point is of extreme importance in the construction of the theory of series.
It is strange that the immense variety in nature can be resolved into a series of numbers. William Henry Bragg, 1923
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Bourchtein, L., Bourchtein, A. (2022). Series of Numbers. In: Theory of Infinite Sequences and Series. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-79431-6_2
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DOI: https://doi.org/10.1007/978-3-030-79431-6_2
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-79430-9
Online ISBN: 978-3-030-79431-6
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