Sequences

• Kenneth A. Ross
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

A sequence is a function whose domain is a set of the form {n ∈ ℤ : n ⩾ m}; m is usually 1 or 0. Thus a sequence is a function that has a specified value for each integer n ⩾ m. It is customary to denote a sequence by a letter such as s and to denote its value at n as s n rather than s(n). It is often convenient to write the sequence as $$({S_n})_{n = m}^\infty or({S_m},{S_{m + 1}},{S_{m + 2}},...)$$. If m = 1 we may write (s n ) n ∈ ℕ or of course (s 1,s 2,s 3,...). Sometimes we will write (s n ) when the domain is understood or when the results under discussion do not depend on the specific value of m. In this chapter we will be interested in sequences whose range values are real numbers, i.e., each s n represents a real number.

Keywords

Rational Number Cauchy Sequence Formal Proof Convergent Sequence Convergent 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 Science+Business Media New York 1980

Authors and Affiliations

• Kenneth A. Ross
• 1
1. 1.Department of MathematicsUniversity of OregonEugeneUSA

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