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Sequences and Difference Equations

Part of the Texts in Computational Science and Engineering book series (TCSE, volume 6)

Abstract

From mathematics you probably know the concept of a sequence, which is nothing but a collection of numbers with a specific order. A general sequence is written as
$$ x_0 ,x_1 ,x_2 , \ldots x_n , \ldots , $$
One example is the sequence of all odd numbers:
$$ 1,3,5,7, \ldots ,2n + 1, \ldots $$
For this sequence we have an explicit formula for the n-th term: 2n+1, and n takes on the values 0, 1, 2., ... We can write this sequence more compactly as (x n ) n=0 with x n =2n+1. Other examples of infinite sequences from mathematics are
$$ 1,4,9,16,25, \ldots \left( {x_n } \right)_{n = 0}^\infty , x_n = \left( {n + 1} \right)^2 , $$
(5.1)
$$ 1,\frac{1} {2},\frac{1} {3},\frac{1} {4} \ldots \left( {x_n } \right)_{n = 0}^\infty , x_n = \frac{1} {{n + 1}}. $$
(5.2)

Keywords

Interest Rate Command Line Logistic Growth Nonlinear Algebraic Equation Secant Method 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

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