Infinite Series of Real Numbers

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


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
$$\sum\limits_{n = 1}^\infty {{a_n} = {a_1} + {a_2} + \cdot \cdot \cdot \,\,\,or\,\,\,\,\,\sum\limits_{k = 0}^\infty {{a_k} = {a_0} + {a_1} + \cdot \cdot \cdot \,\,.} }$$


Positive Integer Ratio Test Nonnegative Integer Infinite Series Cosine Function 
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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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