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Sequence

An infinite sequence is a list that never ends.

Sequences are called infinite because they never stop---there is no last term.

If $\lim a_{n}$ exists, then the sequence $a_{1}$, $a_{2}$, $a_{3}$, $\ldots $, is said to converge. Otherwise, the sequence is said to diverge.

The statement MATHmeans that as $n$ gets large, the difference between $a_{n}$ and $L$ gets arbitrarily small. No matter how large a positive integer $N$ you choose, the numbers in the sequence eventually get within $1/N$ of $L$; that is, there is a positive integer $k$ such that MATH whenever $n>k$.

The statement MATHmeans that as $n$ gets large, the terms $a_{n}$ get arbitrarily large. No matter how large a positive integer $N$ you choose, there is a positive integer $k$ such that $a_{n}>$ $N$ whenever $n>k$.

The statement MATHmeans that MATH.


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Recursive sequence


Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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