Infinite sequences and infinite series

  • M. H. Protter
  • C. B. MorreyJr.
Part of the Undergraduate Texts in Mathematics book series (UTM)


It is customary to use expressions such as
$${u_1} + {u_2} + \cdots + {u_n} + \cdots ,\;and\;\sum\limits_{n = 1}^\infty {{u_n}}$$
to represent infinite series. The u i are called the terms of the series, and the quantities
$${s_n} = {u_1} + {u_2} + \cdots + {u_n},\quad n = 1,2, \ldots ,$$
are called the partial sums of the series. The symbols in (9.1) not only define an infinite series but also are used as an expression for the sum of the series when it converges. To avoid this imprecision we define an infinite series in terms of ordered pairs.


Power Series Uniform Convergence Prove Theorem Finite Subset Infinite Series 
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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • M. H. Protter
    • 1
  • C. B. MorreyJr.
    • 1
  1. 1.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA

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