Sequences and Difference Equations

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


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
$$ 1,4,9,16,25, \ldots \left( {x_n } \right)_{n = 0}^\infty , x_n = \left( {n + 1} \right)^2 , $$
$$ 1,\frac{1} {2},\frac{1} {3},\frac{1} {4} \ldots \left( {x_n } \right)_{n = 0}^\infty , x_n = \frac{1} {{n + 1}}. $$


Interest Rate Command Line Logistic Growth Nonlinear Algebraic Equation Secant Method 
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© Springer-Verlag Berlin Heidelberg 2009

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