A First Course in Real Analysis pp 210-261 | Cite as

# Infinite sequences and infinite series

Chapter

## Abstract

It is customary to use expressions such as to represent infinite series. The are called the

$${u_1} + {u_2} + \cdots + {u_n} + \cdots ,\;and\;\sum\limits_{n = 1}^\infty {{u_n}}$$

(9.1)

*u*_{ i }are called the*terms*of the series, and the quantities$${s_n} = {u_1} + {u_2} + \cdots + {u_n},\quad n = 1,2, \ldots ,$$

*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.## Keywords

Power Series Uniform Convergence Prove Theorem Finite Subset Infinite Series
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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© Springer-Verlag, New York Inc. 1977