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# Infinite Numerical and Functional Series

Chapter
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Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

## Abstract

In Sect. 1.9 we considered summation of finite series. In practice it is often necessary to deal with infinite series which contain an infinite number of terms a n . Here a n is a general (we say “the n-th”) term of the series which is constructed via a some kind of formula depending on an integer n = 1, 2, 3, . For instance, the rule $$a_{n} = a_{0}q^{n}$$ with n = 0, 1, 2, 3,  corresponds to an infinite geometric progression
$$\displaystyle{a_{0} + a_{0}q + a_{0}q^{2} + \cdots = a_{ 0}\left (1 + q + q^{2} + \cdots \,\right ).}$$

## Keywords

Functional Series Infinite Numerical Series Infinite Geometric Progression Harmonic Series Euler-Mascheroni Constant
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Copyright information

© Springer Science+Business Media, LLC 2016

## Authors and Affiliations

1. 1.PhysicsKing’s College LondonLondonUK