A Primer on Scientific Programming with Python pp 235-268 | Cite as

# Sequences and Difference Equations

Chapter

## Abstract

From mathematics you probably know the concept of a One example is the sequence of all odd numbers: For this sequence we have an explicit formula for the

*sequence*, which is nothing but a collection of numbers with a specific order. A general sequence is written as$$
x_0 ,x_1 ,x_2 , \ldots x_n , \ldots ,
$$

$$
1,3,5,7, \ldots ,2n + 1, \ldots
$$

*n*-th term: 2*n*+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 }=2*n*+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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© Springer-Verlag Berlin Heidelberg 2009