Infinite Numerical and Functional Series

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


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
$$\displaystyle{a_{0} + a_{0}q + a_{0}q^{2} + \cdots = a_{ 0}\left (1 + q + q^{2} + \cdots \,\right ).}$$


Functional Series Infinite Numerical Series Infinite Geometric Progression Harmonic Series Euler-Mascheroni Constant 
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© Springer Science+Business Media, LLC 2016

Authors and Affiliations

  1. 1.PhysicsKing’s College LondonLondonUK

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