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Infinite Numerical and Functional Series

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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

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