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Infinite Series of Real Numbers

  • Emanuel Fischer
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

The sums
$$\sum\limits_{k = 1}^n {{a_k} = {a_1} + \cdot \cdot \cdot + {a_n},\,\,\,\,\,\sum\limits_{k = 0}^n {{a_k} = {a_0} + \cdot \cdot \cdot + {a_n},} }$$
where n is some positive integer, were defined in Chapter II. They are examples of finite sums. Now we define the “sum” of the infinite series
$$\sum\limits_{n = 1}^\infty {{a_n} = {a_1} + {a_2} + \cdot \cdot \cdot \,\,\,or\,\,\,\,\,\sum\limits_{k = 0}^\infty {{a_k} = {a_0} + {a_1} + \cdot \cdot \cdot \,\,.} }$$

Keywords

Positive Integer Ratio Test Nonnegative Integer Infinite Series Cosine Function 
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.

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Copyright information

© Springer-Verlag New York, Inc. 1983

Authors and Affiliations

  • Emanuel Fischer
    • 1
  1. 1.Department of MathematicsAdelphi UniversityGarden CityUSA

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